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Quantitative Aptitude ( CCS) Trignometry

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If cos Θ + sin Θ = √2 cos Θ, then cos Θ – sin Θ is

√2 tan Θ

-√2 cos Θ

-√2 sin Θ

√2 sin Θ

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Explanation:

cos Θ + sin Θ = √2 cos Θ
On squaring both sides,
⇒ cos² Θ + sin² Θ + 2 sin Θ cos Θ = 2 cos² Θ
⇒ 2 cos² Θ – cos² Θ – sin² Θ = 2 sin Θ cos Θ
⇒ cos² Θ – sin² Θ = 2 sin Θ cos Θ
⇒ (cos Θ + sin Θ) (cos Θ – sin Θ) = 2 sin Θ cos Θ
⇒ √2 cos Θ (cos Θ – sin Θ) = √2 sin Θ. cos Θ
⇒ (cos Θ – sin Θ) = 2 sin Θ cos Θ /√2 cos Θ
= √2 sin Θ