Question
If cos – sin θ = √2 sin θ, then (cos θ + sin θ)
is:Solution
Given, cos θ -sin θ = √2 sin θ square both sides, we get. Cos2 θ + sin2 θ -2 sin θ cos θ =2 sin θ  1- 2sin θ. cos θ = 2sin2 θ = 2 sin θ cos θ = 1-2 sin² θ .... (i) Now, consider cos θ + sin θ.  By Squaring this expression, we get (cos θ + sin θ)2 = cos2 θ + sin2 θ + 2 sin θ cos θ =1+1-2sin2 θ = 2-2sin2 θ = 2(1 – sin2 θ)  = 2cos2 θ  cos θ + sin θ = √2 cos θ
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