Single Choice

Let P={θ:sin⁡θ−cos⁡θ=2cos⁡θ} and Q={θ:sin⁡θ+cos⁡θ=2sin⁡θ} be two sets. Then:

AP⊂Q and Q−P≠ϕ
BQ⧸⊂P
CP=Q
Correct Answer
DP⧸⊂Q

Solution

sin⁡θ−cos⁡θ=2cos⁡θ
⇒sin⁡θ=cos⁡θ+2cos⁡θ
=(2+1)cos⁡θ=(2−12−1)cos⁡θ
⇒(2−1)sin⁡θ=cos⁡θ
⇒sin⁡θ+cos⁡θ=2sin⁡θ
∴P=Q

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