The value of ^-1((15)/(4)-1()/(4)) is equal to :

Question

The value of $	an^{-1}\left(\dfrac{\cos\frac{15\pi}{4}-1}{\sin\frac{\pi}{4}}ight)$ is equal to :

Accepted Answer

$${\tan ^{ - 1}}\left( {{{\cos \left( {{{15\pi } \over 4}} \right) - 1} \over {\sin {\pi  \over 4}}}} \right)$$

$$ = {\tan ^{ - 1}}\left( {{{{1 \over {\sqrt 2 }} - 1} \over {{1 \over {\sqrt 2 }}}}} \right)$$

$$ = {\tan ^{ - 1}}(1 - \sqrt 2 ) =  - {\tan ^{ - 1}}(\sqrt 2  - 1)$$

$$ =  - {\pi  \over 8}$$

Solutions · 1