Question

if sinQ+cosQ=root2 cosQ then value of tanQ is​

Answer 1

Answer:

hey mate your answer is...

Step-by-step

cos Ф + sin Ф = √2 cos Ф

⇒ sin Ф = cos Ф( √2 – 1)

sin Ф = cosФ ( √2 - 1)( √2+1) ÷ ( √2+1)

sin Ф = cosФ (2 - 1) ÷ √2 + 1

⇒ ( √2 + 1)sin Ф = cos Ф

⇒ √2 sin Ф + sin Ф = cos Ф

⇒ cos Ф – sin Ф = √2 sin Ф

Answer 2

Here

given

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

To find tan@

divide both side by cos@ , we get

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

$= > \tan( \alpha ) + 1 = \sqrt{2} \\ = > \tan( \alpha ) = \sqrt{2} - 1$

hence the value is

$\boxed{ \sqrt{2} - 1}$