Consider the relation in the set P={θ:sinθ−cosθ=√2cosθ} sinθ−cosθ=√2cosθ Dividing both sides by cos θ, we get: tanθ−1=√2 ⇒tanθ=√2+1 ∴P={θ:tanθ=√2+1} .......(1) Consider the relation in the set Q={θ:sinθ+cosθ=√2sinθ}. sinθ+cosθ=√2sinθ Dividing both sides by cosθ, we get: tanθ+1=√2tanθ ⇒tanθ=
1
√2−1
=
1
√2−1
×
√2+1
√2+1
=
√2+1
2−1
=√2+1 ∴Q={θ:tanθ=√2+1} .......(2) Comparing equations (1) and (2), we have: P = Q.