Question

pls answer this question as soon as possible...in step by step ​

Answer 1

$\boxed {\huge \red{ \mathfrak{solution}}}$

Given:

$\sin( \alpha ) + \cos( \alpha ) = \sqrt{2} \cos( \alpha )$

To find

$\tan( \alpha )$

In given value , divide both sides by

$\cos( \alpha )$

we get ,

$\implies \: \frac{ \sin( \alpha ) }{ \cos( \alpha ) } + \frac{ \cos( \alpha ) }{ \cos( \alpha ) } = \sqrt{2} \frac{ \cos( \alpha ) }{ \cos( \alpha ) } \\ \\ \implies \: \tan( \alpha ) + 1 = \sqrt{2} \\ \\ \implies \: \tan( \alpha ) = \sqrt{2} - 1$

Hence the value is

$\huge \purple{\boxed{ \green{\sqrt{2} - 1}}}$

option A is correct

Answer 2

sin@+cos@=√2cos@

divide both sides by cos @

sin@/cos@+cos@/cos@=√2 cos@/cos@

tan@= √2-1