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Question: If the slope of tangent to the curve y = f(x) is \(\frac{\frac{1}{2} - \sin^{2}x}{f(x)}\), then f(x)...

If the slope of tangent to the curve y = f(x) is 12−sin⁡2xf(x)\frac{\frac{1}{2} - \sin^{2}x}{f(x)}, then f(x) is periodic function with principal period –

A

p

B

2p

C

π2\frac{\pi}{2}

D

Non periodic

Answer

p

Explanation

Solution

f ¢(x) = 12−sin⁡2xf(x)\frac{\frac{1}{2} - \sin^{2}x}{f(x)}

On integrating

f(x) = sin⁡2x2+2C\sqrt{\frac{\sin 2x}{2} + 2C}

So f(x) is periodic with period p.