Verified Solution • 2025–26 Session moderate

QJEEM16Mae5c8: JEE Main 2016 Mathematics - Class 11 JEEM16Mae5c8 Solution: Let P = { θ : sin θ − cos θ = 2 cos ⁡ θ } and Q = { θ : sin θ + …

Let P = {θ : sinθ − cosθ = 2cos⁡θ}

and Q = {θ : sinθ + cosθ = 2sin⁡θ} be two sets. Then

Multiple Choice Options

  • A P ⊂ Q and Q − P ≠ ϕ
  • B Q ⊄ P
  • C P ⊄ Q
  • D P = Q

Step-by-Step Verified Solution

Given,

sinθ − cosθ = 2cosθ

⇒   sinθ = (2+1)cosθ

⇒   sinθ = 2−12−1cosθ

⇒   (2−1)sinθ = cosθ      . . . (1)

This is for set P.

sinθ + cosθ = 2sinθ

⇒   cosθ = (2−1)sinθ      . . . .(2)

This is from set Q.

So,   P = Q

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