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If $\sin θ + \cos θ = \sqrt{2} \cos θ$ then $\cos θ - \sin θ$ is equal to

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2 cos θ

2 sin θ

2 (cos θ + sin θ)

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detailed solution

Correct option is B

We have,sin⁡θ+cos⁡θ=2cos⁡θ⇒1+sin⁡2θ=2cos2⁡θ⇒1−sin⁡2θ=2−2cos2⁡θ⇒(cos⁡θ−sin⁡θ)2=2sin2⁡θ⇒cos⁡θ−sin⁡θ=2sin⁡θ

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If sin⁡θ+cos⁡θ=2cos⁡θ then cos⁡θ−sin⁡θis equal to

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If $\sin θ + \cos θ = \sqrt{2} \cos θ$ then $\cos θ - \sin θ$ is equal to