Question

Cos theta + sin theta = √2 cos theta , then show that Cos theta + Sin theta = √2 Sin theta​

Answer 1

here is your answer OK

method is here.......

This is asked as though it is an identity to be proven. In math terms we have

cosθ−sinθ=2sinθ−−−−√ and

cosθ+sinθ=2sinθ−−−−√.

Subtract to get 2sinθ=0 which is an equation to solve, not an identity.

and its identity use OK

and - place + and question answer is here...

let theta = x

cos x + sin x = root2 cos x

squaring on both side, we get......

cos2x + sin2x + 2cosxsinx = 2cos2x

2sinxcosx = 2cos2x - cos2x - sin2x

2sinxcosx = cos2x - sin2x

2sinxcosx = (cosx+sinx) (cosx - sinx)

2sinxcosx = (root2 cosx) (cosx - sinx)

2sinxcosx/root2 cosx = cosx - sinx

root2 sinx = cosx - sinx

Answer 2

Step-by-step explanation:

Let θ = x

cos x  + sin x =  √2 cos x

squaring on both side, we get......

cos2x + sin2x + 2cosxsinx = 2cos2x

2sinxcosx = 2cos2x - cos2x - sin2x

2sinxcosx = cos2x - sin2x

2sinxcosx = (cosx+sinx) (cosx - sinx)

2sinxcosx = (root2 cosx) (cosx - sinx)

2sinxcosx/root2 cosx = cosx - sinx

 √2 sinx = cosx - sinx

Mark me as brilliant if the answer is correct.