1. Tardigrade
  2. Question
  3. Mathematics
  4. The value of sin(2tan-1(0.75)) is equal to

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The value of $sin(2tan^{-1}(0.75))$ is equal to

Inverse Trigonometric Functions

Solution:

Let $2\,tan^{-1}\left(0.75\right) = \theta$
$\Rightarrow 0.75 = tan \left(\frac{\theta}{2}\right)$
$\therefore sin\left(2tan^{-1}\left(0.75\right)\right)$
$= sin\,\theta = \frac{2\,tan\,\theta/2}{1+ tan^{2}\,\theta /2}$
$= \frac{2 \times 0.75}{1+\left(0.75\right)^{2}}$
$= \frac{1.50}{1.5625} $
$= 0.96$