Question

If cosθ + sinθ = √2 cosθ then the value of cosθ – sinθ is what ?​

Answer 1

Answer:

√2 sinx = cosx - sinx

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

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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

thus, cosθ–sinθ=√2sinθ

I hope it will help you