Skolarhive Solution - SkolarHive

Skolarhive Doubt

Ask Question User QA Dashboard DoubtChat

1Vote

1Answer

101View

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

46View

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

44View

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

45View

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

43View

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

44View

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

68View

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

62View

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

Asked by Maths_Expert_3 Nov 11, 2024

0Vote

0Answer

61View

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

Asked by Maths_Expert_3 Nov 11, 2024

0Vote

0Answer

60View

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

Asked by Maths_Expert_3 Nov 11, 2024

0Vote

0Answer

70View

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

Asked by Maths_Expert_3 Nov 11, 2024

0Vote

0Answer

65View

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

55View

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

64View

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

66View

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

96View

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

57View

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

56View

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

77View

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

73View

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

65View

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

66View

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

77View

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

93View

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

89View

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

99View

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

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

0Vote

1Answer

131View

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

119View

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

119View

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

211View

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

77View

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

119View

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

118View

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

123View

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

77View

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

73View

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