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  • The value of sin into bracket 2tan inverse into bracket point .5 is equal to A. point 75 B. 1 point 5 C. point96 D. sin 1 point 5

The value of sin (2tan–1 (.75)) is equal to
A. 0.75
B. 1.5
C. 0.96
D. sin 1.5

Answers (1)

Answer :(c)

sin (2tan–1 (.75))

Let, tan–1 (.75) = θ

\Rightarrow \tan^{-1}\left (\frac{3}{4} \right )=\theta

\Rightarrow \tan \theta =\frac{3}{4}

As, \tan \theta =\frac{3}{4} so

\sin \theta =\frac{3}{5}, \cos \theta =\frac{4}{5}......(1)

Now,

sin (2tan–1 (.75)) = sin 2θ

= 2 sin θ cos θ

=2\left (\frac{3}{5} \right )\left (\frac{4}{5} \right )

=\frac{24}{25}
So, sin (2tan–1 (.75)) = 0.96.

Posted by

infoexpert24

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