Question

The value of sin (2 tan^–1(0.75)) is equal to ______.

विकल्प

• 0.75

• 1.5

• 0.96

• sin 1.5

Answer 1

The value of sin (2 tan^–1(0.75)) is equal to 0.96.

Explanation:

We have, sin [2 tan^–1(0.75))]

= `sin(2 tan^-1  3/4)`

= `sin(sin^-1  (2* 3/4)/(1 + 9/16))` ......`(because 2 tan^-1x = sin^-1  (2x)/(1 + x^2))`

= `sin(sin^-1  (3/2)/(25/16))`

= `sin(sin^-1  24/25)`

= `24/25`

= 0.96