Question

Which of the following numbers is the maximum value of the function f(x) = $\frac{5\sin^{3}x\cos x}{\tan^{2}x + 1}$, $\forall$ x Î R ?

• A. 5/8
• B. ¾
• C. 1
• D. 5/ 2

Answer 1

Answer: (A)

5/8

Answer 2

Given, f(x) = $\frac{5\sin^{3}x\cos x}{\tan^{2}x + 1}$ = $\frac{5\sin^{3}x\cos x}{\frac{\sin^{2}x}{\cos^{2}x} + 1}$

= 5(sin³x) (cos³x) = $\frac{5}{8}\sin^{3}2x$

Hence maximum value is $\frac{5}{8}$.