Question

simplify tan^-1(cosx-sinx/cosx+sinx)​

Answer 1

Answer:

$\frac{\pi}{4} - x$

Step-by-step explanation:

$\tan { - }^{1} ( \frac{ cosx- sinx} { cosx + sinx} )$

${ \tan - }^{1} ( \frac{ cosx - sinx }{ cosx + sinx} )$

${ \tan- }^{1} ( \frac{ \frac{ cosx - sinx }{ cosx } }{ \frac{ cosx + sinx }{ { cosx } } } )$

${ \tan - }^{1} ( \frac{ \frac{ cosx }{ cosx } - \frac{ sinx}{ cosx} }{ \frac{ cosx}{ cosx } + \frac{ sinx }{ cosx} } )$

${ \tan - }^{1} ( \frac{1 - tanx }{1 - tanx } )$

${ \tan- }^{1} ( \frac{1 - tanx}{1 + 1. tanx } )$

${ \tan- }^{1} ( \frac{ \tan( \frac{\pi}{4} - tanx }{1 + \tan( \frac{\pi}{4. tanx } } )$

${ \tan - }^{1} ( \tan( \frac{\pi}{4 } - x))$

$\frac{\pi}{4} - x$