IIT-JEE 2011 · Paper 1 · Mathematics Q50

← IIT-JEE 2011 · Paper 1

MathematicsSingle correct+3 / -1Question 50 of 69

Let $P=\left\{\theta:\sin\theta-\cos\theta=\sqrt2\cos\theta\right\}$ and $Q=\left\{\theta:\sin\theta+\cos\theta=\sqrt2\sin\theta\right\}$ be two sets. Then

P\subset Q

and

Q-P\ne\emptyset

Q\not\subset P

P\not\subset Q

P=Q

Answer and worked solution

Official answer: D

P: $\sin\theta=(1+\sqrt2)\cos\theta$ , i.e. $\tan\theta=\sqrt2+1$ .

Q: $(\sqrt2-1)\sin\theta=\cos\theta$ , i.e. $\tan\theta=\dfrac1{\sqrt2-1}=\sqrt2+1$ .

Same condition, so $P=Q$ .

(D)

Topics:Trigonometric equations

← Previous question Next question →

IIT-JEE 2011 · Paper 1, Mathematics question 50