Question

The period of the function

f(x) = `(sin 8x cos x - sin 6x cos 3x)/(cos 2x cos x - sin 3x sin 4x)` is ______.

विकल्प

• π

• 2π

• `π/2`

• None of these

Answer 1

The period of the function

f(x) = `(sin 8x cos x - sin 6x cos 3x)/(cos 2x cos x - sin 3x sin 4x)` is `underlinebb(π/2)`.

Explanation:

Given, f(x) = `(sin 8x cos x - sin 6x cos 3x)/(cos 2x . cos x - sin 3x . sin 4x)`

= `(2 sin 8x cos x - 2 sin 6x cos 3x)/(2 cos 2x cos x - 2 sin 3x sin 4x)`

= `((sin 9x + sin 7x) - (sin 9x + sin 3x))/((cos 3x + cos x) + (cos 7x - cos x))`

= `(sin 7x - sin 3x)/(cos 7x + cos 3x)`

= `(2 cos 5x sin 2x)/(2 cos 2x cos 5x)`

= tan 2x

∴ Period of f(x) = `π/2`