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Prove that \(1+\frac{\cot^2 \alpha}{1+\text{cosec} \alpha}=\text{cosec} \alpha\)

Solved Asked by Maths_Expert_3 Mar 30, 2025 Last replied by Maths_Expert_3

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Prove that \( \left( \sqrt{3}+1\right) \left(3- \cot 30^{\omicron}\right)=\tan^3 60^{\omicron}-2\sin 60^{\omicron}\)

Solved Asked by Maths_Expert_3 Mar 30, 2025 Last replied by Maths_Expert_3

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Prove that \( (\sin \alpha +\cos \alpha)(\tan \alpha + \cot \alpha)=\sec \alpha +\text{cosec} \alpha \)

Solved Asked by Maths_Expert_3 Mar 29, 2025 Last replied by Maths_Expert_3

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If \( \tan A = \frac{3}{4}\), then \(\sin A \cos A= \frac{12}{25}\)

Solved Asked by Maths_Expert_3 Mar 29, 2025 Last replied by Maths_Expert_3

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Prove that \( \frac{\tan A}{1+\sec A}-\frac{\tan A}{1-\sec A}=2 \text{cosec} A \)

Solved Asked by Maths_Expert_3 Mar 29, 2025 Last replied by Maths_Expert_3

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Prove that \( \frac{\sin \theta}{1+\cos \theta}+\frac{1+\cos \theta}{\sin \theta}=2 \text{cosec} \theta \)

Solved Asked by Maths_Expert_3 Mar 29, 2025 Last replied by Maths_Expert_3

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The number of real roots of the equation \(\sqrt{x^2-4x+3}+\sqrt{x^2-9}=\sqrt{4x^2-14x+6}\), is (a) 3 (b) 2 (c) 0 (d) 1

Asked by Maths_Expert_3 Nov 08, 2024 Last replied by Maths_Expert_3

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The value of \((128^{-\frac{2}{7}})^{\frac{(64)^\frac{2}{12}}{2}\)

Asked by Maths_Expert_3 Nov 11, 2024

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Find the value of \(p\) if \(5^{p-3}=125^{2p-6}\).

Asked by Maths_Expert_3 Nov 11, 2024

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The value of \(2^{2^{2^2}}\) is

Asked by Maths_Expert_3 Nov 11, 2024

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If \(x^{x^{\frac{3}{2}}}=(x^{\frac{3}{2}})^x\) then \(x=?\).

Asked by Maths_Expert_3 Nov 11, 2024

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The number of real solutions of the equation \(|x|^2-3|x|+2=0\) is

Asked by Maths_Expert_3 Nov 08, 2024

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The equation \( \sqrt{x+1}-\sqrt{x-1}=\sqrt{4x-1}\) has (a) no solution (b) one solution (c) two solutions (d) more than two solutions

Asked by Maths_Expert_3 Nov 08, 2024

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The equation \(x-\frac{2}{x-1}=1-\frac{2}{x-1}\) has (a) no root (b) one root (c) two equal roots (d) infinitely many roots

Asked by Maths_Expert_3 Nov 08, 2024

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The sum of all roots of the equation \(|x^2-8x+15|-2x+7=0\) is

Asked by Maths_Expert_3 Nov 08, 2024

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If the sum of the first \(2n\) terms of AP series \(2,5,8,…,\) is equal to the sum of the first \(n\) terms of the AP series \(57, 59, 61,…,\) then \(n\) equals

Asked by Maths_Expert_3 Nov 08, 2024

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If the sum of \(n\) terms of an AP is \(cn^2\), then the sum of squares of these \(n\) terms is

Asked by Maths_Expert_3 Nov 08, 2024

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If \(\log_4A=\log_6B=\log_9(A+B)\), then the value of \(\frac{B}{A}\) is

Asked by Maths Expert_1 Nov 07, 2024

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The number of solutions of \(\log_4(x-1)=\log_2(x-3)\). (a) 3 (b) 1 (c) 2 (d) 0

Solved Asked by Maths_Expert_3 Nov 05, 2024 Last replied by Maths_Expert_3

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If \(x^2-10ax-11b=0\) have roots \(c\) and \(d\). \(x^2-10cx-11d=0\) have roots \(a\) and \(b\), then find \(\a+b+c+d\).

Asked by Maths_Expert_3 Nov 05, 2024

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If \(x^4+\frac{1}{x^4}=727\), then the value of \(x^3-\frac{1}{x^3}\).

Solved Asked by Maths_Expert_3 Nov 03, 2024 Last replied by Maths_Expert_3

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If \(x+\frac{1}{x}=3\), then the value of \(x^2+\frac{1}{x^2}\).

Asked by Maths_Expert_3 Nov 03, 2024

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Prove that \(\frac{1}{1+p+q^{-1}}+\frac{1}{1+q+r^{-1}}+\frac{1}{1+r+p^{-1}}=1\), if \(pqr=1\)

Solved Asked by Maths_Expert_3 Oct 31, 2024 Last replied by Maths_Expert_3

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If \(a^x=b^y=c^z\) and \(b^2=ac\) then \(y\) equals? a) \(\frac{2xz}{(x+z)}\). b) \(\frac{xz}{2(x-z)}\). c) \(\frac{xz}{2(z-x)}\). d) \(\frac{2xz}{(x-z)}\)

Asked by Maths Expert_1 Sep 24, 2024 Last replied by Maths_Expert_3

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If \(a^x=b^y=c^z \quad \text{and} \quad b^2=ac\) then \(y\) equals? a) \(\frac{2xz}{(x+z)}\) b) \(\frac{xz}{2(x-z)}\) c) \(\frac{xz}{2(z-x)}\) d) \(\frac{2xz}{(x-z)}\)

Asked by Maths Expert_1 Sep 24, 2024 Last replied by Maths_Expert_3

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If \(x^x=2^{2048}\), find \(x\).

Asked by Maths Expert_1 Sep 23, 2024 Last replied by Maths_Expert_3

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If α, β are the zeroes of the polynomial \(f(x)=x^2-p(x+1)-q\), then ( α+1)(β +1)=

Asked by Maths_Expert_3 Oct 13, 2024 Last replied by Maths_Expert_3

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If α, β are the zeroes of the polynomial \(f(x)=ax^2+bx+c\), then \(\frac{1}{α^2}+\frac{1}{β^2}=?\)

Asked by Maths_Expert_3 Oct 13, 2024 Last replied by Maths_Expert_3

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If sum of the zeroes = α+β = – 8 and product of zeroes = αβ = 6, then the polynomial whose zeroes are \(\frac{1}{α}\) and \(\frac{1}{β}\) is

Asked by Maths_Expert_3 Oct 13, 2024 Last replied by Maths_Expert_3

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If α, β are the zeroes of the polynomial \(f(x)=ax^2+bx+c\), then \(\sqrt{\frac{α}{β}}+\sqrt{\frac{β}{α}}=?\)

Asked by Maths_Expert_3 Oct 13, 2024 Last replied by Maths_Expert_3

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If(x-4) is a factor of a quadratic polynomial p(x) and 2 is zero of p(x), then find the polynomial p(x).

Solved Asked by Maths_Expert_3 Oct 13, 2024 Last replied by Maths_Expert_3

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If α and β are the zeroes of the polynomial \(x^2+5x+c\), and \( α-β=3\), then \(c=\)? a) 0 b) 1 c) 4 d) 5

Asked by Maths_Expert_3 Oct 12, 2024 Last replied by Maths_Expert_3

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If α and β are the zeroes of the polynomial \(x^2+5x+c\), and \( α-β=2\), then \(c=\)? a) 0 b) \(-\frac{21}{4}\) c) \(\frac{21}{4}\) d) 5

Asked by Maths_Expert_3 Oct 12, 2024 Last replied by Maths_Expert_3

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If α and β are the zeroes of the polynomial \(2x^2+4x+5\), then find the value of \(α^3+β^3\).

Asked by Maths_Expert_3 Oct 12, 2024 Last replied by Maths_Expert_3

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Exercise 7.4 Integrate the function \(\frac{3x}{1+2x^4}\)

Asked by Maths_Expert_3 Oct 04, 2024 Last replied by Maths_Expert_3

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Exercise 7.4 Integrate the function \(\frac{6x+7}{\sqrt{(x-5)(x-4)}}\)