Skolarhive Solution - SkolarHive

Skolarhive Doubt

Ask Question User QA Dashboard DoubtChat

1Vote

1Answer

147View

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

87View

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

93View

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

89View

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

79View

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

88View

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

109View

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

107View

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

Asked by Maths_Expert_3 Nov 11, 2024

0Vote

0Answer

101View

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

Asked by Maths_Expert_3 Nov 11, 2024

0Vote

0Answer

106View

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

Asked by Maths_Expert_3 Nov 11, 2024

0Vote

0Answer

121View

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

Asked by Maths_Expert_3 Nov 11, 2024

0Vote

0Answer

125View

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

99View

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

106View

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

117View

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

174View

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

100View

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

98View

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

131View

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

127View

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

126View

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

118View

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

121View

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

151View

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

157View

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

160View

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

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

0Vote

1Answer

196View

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

208View

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

207View

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

314View

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

119View

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

191View

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

197View

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

215View

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

112View

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

119View

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