Question

if cos theta+sin theta=root 2 cos theta show that cis theta-Sin theta=root 2 sin theta​

Answer 1

Answer:

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

Answer 2

Answer:

If cosθ+sinθ=2cosθ, show that cosθ−sinθ=2sinθ.

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ANSWER

Given,

cosθ+sinθ=2cosθ

squaring on both the sides, we get,

cos2θ+sin2θ+2sinθcosθ=2cos2θ

cos2θ−sin2θ=2cosθsinθ

(cosθ+sinθ)(cosθ−sinθ)=2cosθsinθ

2cosθ(cosθ−sinθ)=2cosθsinθ     [ Given cosθ+sinθ=2cosθ]

∴cosθ−sinθ=2sinθ   [henceproved]