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Question
The value of sin (2 tan–1(0.75)) is equal to ______.
Options
0.75
1.5
0.96
sin 1.5
Solution
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
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