Question & Answer - Recent questions tagged প্রমাণ https://qna.enoteshare.com/tag/%E0%A6%AA%E0%A7%8D%E0%A6%B0%E0%A6%AE%E0%A6%BE%E0%A6%A3 Powered by Question2Answer $\frac{a}{x}=\frac{b}{y}=\frac{c}{z}$ হলে প্রমাণ কর যে, $\frac{a^3+b^3+c^3}{x^3+y^3+z^3}=\frac{abc}{xyz}$ https://qna.enoteshare.com/19374/ Math https://qna.enoteshare.com/19374/ Sat, 13 Dec 2025 12:24:31 +0000 যদি $a:b=b:c$ হয়, তবে প্রমাণ কর যে, $\frac{a}{c}=\frac{a^2+b^2}{b^2+c^2}$ https://qna.enoteshare.com/17453/ Algebra https://qna.enoteshare.com/17453/ Sun, 07 Sep 2025 18:19:17 +0000 যদি $a:b=b:c$ হয়, তবে প্রমাণ কর যে, $a^2b^2c^2\left(\frac{1}{a^3}+\frac{1}{b^3}+\frac{1}{c^3}\right)$$=a^3+b^3+c^3$ https://qna.enoteshare.com/17452/ Algebra https://qna.enoteshare.com/17452/ Sun, 07 Sep 2025 18:18:50 +0000 যদি $a:b=b:c$ হয়, তবে প্রমাণ কর যে, $\frac{abc\left(a+b+c\right)^3}{\left(ab+bc+ca\right)^3}=1$ https://qna.enoteshare.com/17451/ Algebra https://qna.enoteshare.com/17451/ Sun, 07 Sep 2025 18:18:24 +0000 $x=\frac{\sqrt[3]{m+1}+\sqrt[3]{m-1}}{\sqrt[3]{m+1}-\sqrt[3]{m-1}}$ হলে, প্রমাণ কর যে, $x^3-3mx^2+3x-m=0$ https://qna.enoteshare.com/17444/ Algebra https://qna.enoteshare.com/17444/ Sun, 07 Sep 2025 18:13:10 +0000 $\frac{x}{b+c}=\frac{y}{c+a}=\frac{z}{a+b}$ হলে, প্রমাণ কর যে, $\frac{a}{y+z-x}=\frac{b}{z+x-y}=\frac{c}{x+y-z}$। https://qna.enoteshare.com/17441/ Algebra https://qna.enoteshare.com/17441/ Sun, 07 Sep 2025 18:12:18 +0000 $\frac{bz-cy}{a}=\frac{cx-az}{b}=\frac{ay-bx}{c}$ হলে, প্রমাণ কর যে, $\frac{x}{a}=\frac{y}{b}=\frac{z}{c}$। https://qna.enoteshare.com/17440/ Algebra https://qna.enoteshare.com/17440/ Sun, 07 Sep 2025 18:11:55 +0000 $\frac{a+b-c}{a+b}=\frac{b+c-a}{b+c}=\frac{c+a-b}{c+a}$ এবং $a+b+c \neq 0$ হলে, প্রমাণ কর যে, $a=b=c$ https://qna.enoteshare.com/17439/ Algebra https://qna.enoteshare.com/17439/ Sun, 07 Sep 2025 18:11:37 +0000 যদি $(a+b+c)p=$$(b+c-a)q=$$(c+a-b)r=$$(a+b-c)s$ হয়, তবে প্রমাণ কর যে, $\frac{1}{q}+\frac{1}{r}+\frac{1}{s}=\frac{1}{p}$। https://qna.enoteshare.com/17437/ Algebra https://qna.enoteshare.com/17437/ Sun, 07 Sep 2025 18:10:51 +0000 প্রমাণ কর যে: $\dfrac{4^{n}-1}{2^{n}-1}=2^{n}+1$ https://qna.enoteshare.com/14857/ Algebra https://qna.enoteshare.com/14857/ Tue, 22 Jul 2025 16:02:36 +0000 প্রমাণ কর যে: $\frac{a^{p+q}}{a^{2r}}\times\frac{a^{q+r}}{a^{2p}}\times\frac{a^{r+p}}{a^{2q}}=1$ https://qna.enoteshare.com/14856/ Algebra https://qna.enoteshare.com/14856/ Tue, 22 Jul 2025 16:01:22 +0000 প্রমাণ কর যে: $\dfrac{2^{2p+1}\cdot3^{2p+q}\cdot5^{p+q}\cdot6^{p}}{3^{p-2}\cdot6^{2p+2}\cdot10^{p}\cdot15^{q}}=\dfrac12$ https://qna.enoteshare.com/14855/ Algebra https://qna.enoteshare.com/14855/ Tue, 22 Jul 2025 15:58:43 +0000 প্রমাণ কর যে: $\left(\frac{x^{a}}{x^{b}}\right)^{\frac{1}{ab}}\cdot\left(\frac{x^{b}}{x^{c}}\right)^{\frac{1}{bc}}\cdot\left(\frac{x^{c}}{x^{a}}\right)^{\frac{1}{ca}}=1$ https://qna.enoteshare.com/14854/ Algebra https://qna.enoteshare.com/14854/ Tue, 22 Jul 2025 15:55:30 +0000 প্রমাণ কর যে: $\left(\frac{a^{l}}{a^{m}}\right)^{n}\cdot\left(\frac{a^{m}}{a^{n}}\right)^{l}\cdot\left(\frac{a^{n}}{a^{l}}\right)^{m}=1$ https://qna.enoteshare.com/14853/ Algebra https://qna.enoteshare.com/14853/ Tue, 22 Jul 2025 15:52:48 +0000 প্রমাণ কর যে: $\left(\frac{x^{a}}{x^{b}}\right)^{a+b}\cdot\left(\frac{x^{b}}{x^{c}}\right)^{b+c}\cdot\left(\frac{x^{c}}{x^{a}}\right)^{c+a}=1$ https://qna.enoteshare.com/14852/ Algebra https://qna.enoteshare.com/14852/ Tue, 22 Jul 2025 15:50:31 +0000 প্রমাণ কর যে: $\left(\frac{x^{p}}{x^{q}}\right)^{p+q-r}\cdot\left(\frac{x^{q}}{x^{r}}\right)^{q+r-p}$$\cdot\left(\frac{x^{r}}{x^{p}}\right)^{r+p-q}$$=1$ https://qna.enoteshare.com/14851/ Algebra https://qna.enoteshare.com/14851/ Tue, 22 Jul 2025 15:46:50 +0000 $x-\frac1x=4$ হলে প্রমাণ কর যে, $x^4+\frac1{x^4}=322$ https://qna.enoteshare.com/14380/ Algebra https://qna.enoteshare.com/14380/ Sat, 05 Jul 2025 15:15:10 +0000 $a+b=\sqrt7$ এবং $a-b=\sqrt5$ হলে, প্রমাণ কর যে, $8ab(a^2+b^2)=24$ https://qna.enoteshare.com/14377/ Algebra https://qna.enoteshare.com/14377/ Sat, 05 Jul 2025 15:09:31 +0000 $sin^4A+sin^2A=1$ হলে, প্রমাণ কর যে, $tan^4A-tan^2A=1$ https://qna.enoteshare.com/14277/ Trigonometry https://qna.enoteshare.com/14277/ Thu, 26 Jun 2025 06:40:52 +0000 $cot^4A-cot^2A=1$ হলে, প্রমাণ কর যে, $cos^4A+cos^2A=1$ https://qna.enoteshare.com/14276/ Trigonometry https://qna.enoteshare.com/14276/ Thu, 26 Jun 2025 06:38:58 +0000 $tanA+sinA=a$ এবং $tanA-sinA=b$ হলে, প্রমাণ কর যে, $a^2-b^2=4\sqrt{ab}$ https://qna.enoteshare.com/14275/ Trigonometry https://qna.enoteshare.com/14275/ Thu, 26 Jun 2025 06:35:21 +0000 প্রমাণ কর: $\sqrt{\frac{1-sinA}{1+sinA}}$$=secA-tanA$ https://qna.enoteshare.com/14274/ Trigonometry https://qna.enoteshare.com/14274/ Thu, 26 Jun 2025 06:24:52 +0000 প্রমাণ কর: $\frac{tanA}{secA+1}-\frac{secA-1}{tanA}=0$ https://qna.enoteshare.com/14273/ Trigonometry https://qna.enoteshare.com/14273/ Thu, 26 Jun 2025 06:21:32 +0000 প্রমাণ কর: $\frac{1}{2-sin^2\theta}+\frac{1}{2+tan^2\theta}=1$ https://qna.enoteshare.com/14272/ Trigonometry https://qna.enoteshare.com/14272/ Thu, 26 Jun 2025 06:19:37 +0000 প্রমাণ কর যে, $\frac{1}{1+sin^2\theta}+\frac{1}{1+cosec^2\theta}=1$ https://qna.enoteshare.com/14271/ Trigonometry https://qna.enoteshare.com/14271/ Thu, 26 Jun 2025 06:08:08 +0000 প্রমাণ কর যে, $sec^2\theta+cosec^2\theta=$$sec^2\theta \cdot cosec^2\theta$ https://qna.enoteshare.com/14270/ Trigonometry https://qna.enoteshare.com/14270/ Thu, 26 Jun 2025 05:59:20 +0000 প্রমাণ কর যে, $tan\theta + cot \theta= $$sec \theta \cdot cosec \theta$ https://qna.enoteshare.com/14269/ Trigonometry https://qna.enoteshare.com/14269/ Thu, 26 Jun 2025 05:18:09 +0000 $ABC$ সমকোণী ত্রিভুজের $\angle B=$ এক সমকোণ এবং $cot A + cot B = 2 cot C$ হলে প্রমাণ কর যে, $AC^2+BC^2=2AB^2$ https://qna.enoteshare.com/14251/ Trigonometry https://qna.enoteshare.com/14251/ Mon, 23 Jun 2025 15:38:10 +0000 $ABC$ সমকোণী ত্রিভুজের $\angle B=$ এক সমকোণ এবং $AC = BC$ হলে প্রমাণ কর যে, $\frac{BC cos C - AC cos B}{BC cos B - AC cos A}$$+cosC=0$ https://qna.enoteshare.com/14250/ Trigonometry https://qna.enoteshare.com/14250/ Mon, 23 Jun 2025 15:36:34 +0000 $cos\theta=\frac{1}{2}$ হলে $cot\theta$ এর মান কোনটি? https://qna.enoteshare.com/14249/ Trigonometry https://qna.enoteshare.com/14249/ Mon, 23 Jun 2025 15:34:38 +0000 $cosA+sinA=\sqrt2 cosA$ হলে, তবে প্রমাণ কর যে, $cosA-sinA=\sqrt2 sinA$ https://qna.enoteshare.com/13863/ Trigonometry https://qna.enoteshare.com/13863/ Mon, 16 Jun 2025 15:36:58 +0000 প্রমাণ কর যে, $\sqrt{\frac{secA+1}{secA-1}}=cotA+cosecA$ https://qna.enoteshare.com/13860/ Trigonometry https://qna.enoteshare.com/13860/ Mon, 16 Jun 2025 15:20:58 +0000 প্রমাণ কর যে, $\sqrt{\frac{1-sinA}{1+sinA}}=secA-tanA$ https://qna.enoteshare.com/13857/ Trigonometry https://qna.enoteshare.com/13857/ Mon, 16 Jun 2025 15:03:02 +0000 প্রমাণ কর যে, $\frac{cotA+tanB}{cotB+tanA}=cotA \cdot tanB$ https://qna.enoteshare.com/13854/ Trigonometry https://qna.enoteshare.com/13854/ Mon, 16 Jun 2025 14:53:12 +0000 প্রমাণ কর যে, $(tan\theta+sec\theta)^2=\frac{1+sin\theta}{1-sin\theta}$ https://qna.enoteshare.com/13851/ Trigonometry https://qna.enoteshare.com/13851/ Mon, 16 Jun 2025 14:39:38 +0000 প্রমাণ কর যে, $\frac{tanA}{secA+1}-\frac{secA-1}{tanA}=0$ https://qna.enoteshare.com/13849/ Trigonometry https://qna.enoteshare.com/13849/ Mon, 16 Jun 2025 14:28:39 +0000 প্রমাণ কর যে, $\frac{sinA}{1-cosA}+\frac{1-cosA}{sinA}$$=2cosecA$ https://qna.enoteshare.com/13833/ Trigonometry https://qna.enoteshare.com/13833/ Mon, 16 Jun 2025 14:14:47 +0000 প্রমাণ কর যে, $\frac{1}{cosecA-1}-\frac{1}{cosecA+1}=2tan^2A$ https://qna.enoteshare.com/13808/ Trigonometry https://qna.enoteshare.com/13808/ Mon, 16 Jun 2025 14:02:26 +0000 প্রমাণ কর যে, $\frac{1}{1+sinA}+\frac{1}{1-sinA}=2sec^2A$ https://qna.enoteshare.com/13791/ Trigonometry https://qna.enoteshare.com/13791/ Mon, 16 Jun 2025 13:42:03 +0000 প্রমাণ কর যে, $\frac{cosecA}{cosecA-1}+\frac{cosecA}{cosecA+1}=2sec^2A$ https://qna.enoteshare.com/13789/ Trigonometry https://qna.enoteshare.com/13789/ Mon, 16 Jun 2025 13:07:36 +0000 প্রমাণ কর যে, $\frac{secA+tanA}{cosecA+cotA}=\frac{cosecA-cotA}{secA-tanA}$ https://qna.enoteshare.com/13786/ Trigonometry https://qna.enoteshare.com/13786/ Mon, 16 Jun 2025 12:54:19 +0000 প্রমাণ কর যে, $tanA\sqrt{1-sin^2A}=sinA$ https://qna.enoteshare.com/13782/ Trigonometry https://qna.enoteshare.com/13782/ Mon, 16 Jun 2025 12:41:58 +0000 প্রমাণ কর যে, $\frac{cosA}{1-tanA}+\frac{sinA}{1-cotA}$$=sinA+cosA$ https://qna.enoteshare.com/13780/ Trigonometry https://qna.enoteshare.com/13780/ Mon, 16 Jun 2025 12:26:57 +0000 প্রমাণ কর যে, $\frac{1}{1+tan^2A}+\frac{1}{1+cot^2A}=1$ https://qna.enoteshare.com/13773/ Trigonometry https://qna.enoteshare.com/13773/ Mon, 16 Jun 2025 11:22:14 +0000 প্রমাণ কর যে, $\frac{tanA}{1-cotA}+\frac{cotA}{1-tanA}$$=secAcosecA+1$ https://qna.enoteshare.com/13772/ Trigonometry https://qna.enoteshare.com/13772/ Mon, 16 Jun 2025 11:20:16 +0000 প্রমাণ কর যে, $\frac{1}{1+sin^2A}+\frac{1}{1+cosec^2A}=1$ https://qna.enoteshare.com/13757/ Trigonometry https://qna.enoteshare.com/13757/ Sun, 15 Jun 2025 16:44:08 +0000 প্রমাণ কর যে, $\frac{secA}{cosA}-\frac{tanA}{cotA}=1$ https://qna.enoteshare.com/13756/ Trigonometry https://qna.enoteshare.com/13756/ Sun, 15 Jun 2025 16:42:29 +0000 প্রমাণ কর যে, $\frac{sinA}{cosecA}+\frac{cosA}{secA}=1$ https://qna.enoteshare.com/13755/ Trigonometry https://qna.enoteshare.com/13755/ Sun, 15 Jun 2025 16:41:21 +0000 প্রমাণ কর যে, $\frac{1}{cos^2A}-\frac{1}{cot^2A}=1$ https://qna.enoteshare.com/13752/ Trigonometry https://qna.enoteshare.com/13752/ Sun, 15 Jun 2025 16:33:38 +0000 প্রমাণ কর যে, $\frac{1}{sin^2A}-\frac{1}{tan^2A}=1$ https://qna.enoteshare.com/13749/ Trigonometry https://qna.enoteshare.com/13749/ Sun, 15 Jun 2025 16:22:33 +0000