Question

If $\tan \theta=\sqrt{\frac{ a }{ b }}$ where $a , b$ are positive reals then the value of $\sin \theta \sec ^7 \theta+\cos \theta \text{cosec}^7 \theta$ is -

• A. $\frac{(a+b)^3\left(a^4+b^4\right)}{(a b)^{7 / 2}}$
• B. $\frac{(a+b)^3\left(a^4-b^4\right)}{(a b)^{7 / 2}}$
• C. $\frac{(a+b)^3\left(b^4-a^4\right)}{(a b)^{7 / 2}}$
• D. $-\frac{( a + b )^3\left( a ^4+ b ^4\right)}{( ab )^{7 / 2}}$

Answer 1

Answer: (A)

Correct answer is (a) $\frac{(a+b)^3\left(a^4+b^4\right)}{(a b)^{7 / 2}}$