Skolarhive Solution - SkolarHive

Skolarhive Doubt

Ask Question User QA Dashboard DoubtChat

1Vote

1Answer

121View

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

1Vote

1Answer

63View

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

1Vote

1Answer

66View

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

1Vote

1Answer

63View

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

1Vote

1Answer

59View

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

1Vote

1Answer

63View

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

0Vote

1Answer

87View

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

0Vote

0Answer

79View

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

Asked by Maths_Expert_3 Nov 11, 2024

0Vote

0Answer

78View

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

Asked by Maths_Expert_3 Nov 11, 2024

0Vote

0Answer

85View

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

Asked by Maths_Expert_3 Nov 11, 2024

0Vote

0Answer

84View

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

Asked by Maths_Expert_3 Nov 11, 2024

0Vote

0Answer

97View

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

Asked by Maths_Expert_3 Nov 08, 2024

0Vote

0Answer

73View

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

0Vote

0Answer

84View

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

0Vote

0Answer

88View

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

Asked by Maths_Expert_3 Nov 08, 2024

0Vote

0Answer

137View

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

0Vote

0Answer

71View

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

0Vote

0Answer

73View

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

1Vote

1Answer

102View

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

0Vote

0Answer

92View

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

1Vote

2Answer

98View

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

0Vote

0Answer

81View

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

Asked by Maths_Expert_3 Nov 03, 2024

1Vote

1Answer

102View

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

1Vote

1Answer

110View

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

0Vote

0Answer

124View

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

0Vote

1Answer

125View

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

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

0Vote

1Answer

155View

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

0Vote

1Answer

140View

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

0Vote

1Answer

143View

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

0Vote

1Answer

239View

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

1Vote

1Answer

96View

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

0Vote

1Answer

141View

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

0Vote

1Answer

138View

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

0Vote

1Answer

151View

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

1Vote

1Answer

90View

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

0Vote

0Answer

96View

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