# Math Help - inverse trigonometry

1. ## inverse trigonometry

Show that 2sin-1(3/5) = sin-1(24/25)

any help is greatly appreciated ! thankyou !

2. Originally Posted by iiharthero
Show that 2sin-1(3/5) = sin-1(24/25)

any help is greatly appreciated ! thankyou !
it is the first time I solved something like this

$\sin ^{-1} \left(\frac{3}{5}\right) = u$

$\frac{3}{5} = \sin u$

$\cos u = \frac{4}{5}$

$\sin u \cos u = \frac{3}{5}\left(\frac{4}{5}\right)$

$\sin u \cos u = \frac{12}{25}$

$\frac{\sin 2u }{2} = \frac{12}{25}$

$\sin 2u = \frac{24}{25}$

$2u=\sin ^{-1} \left(\frac{24}{25}\right)$

but
$u=\sin ^{-1} \left(\frac{3}{5}\right)$

$2\sin ^{-1} \left(\frac{3}{5}\right)=\sin ^{-1} \left(\frac{24}{25}\right)$

3. Let $\frac{3}{5}=sin\theta$

$cos\theta=\frac{4}{5}$

$sin2\theta=2sin\theta cos\theta$

$sin2\theta=2*\frac{3}{5}*\frac{4}{5}$

$sin2\theta=\frac{24}{25}$

$2\theta=sin^{-1}{\frac{24}{25}}$

$2sin^{-1}{\frac{3}{5}}=sin^{-1}{\frac{24}{25}}$