Assertion ( A ) : If 4 sin 4 θ + sin 2 2 θ + 4 cos 2 π 4 - θ 2 = 2 , then θ lies in…

Assertion (A): If 4sin4θ+sin22θ+4cos2π4-θ2=2, then θ lies in 3rd quadrant or 4th quadrant.
Reason R: sin2θ=sinθ
  1. Both (A) and (R) are true and (R) is the correct explanation of (A)
  2. Both (A) and (R) are true but (R) is not the correct explanation of (A)
  3. (A) is true but (R) is false
  4. (A) is false but (R) is true

Solution

Assertion given:-

4sin4θ+sin22θ+4cos2π2-θ2=2

Simplify the above expression.

4sin4θ+4sin2θcos2θ+21+cos2π2-θ2=2

⇒4sin2θsin2θ+cos2θ+2{1+sinθ}=2

⇒4sin2θ+2+2sinθ=2

⇒|2sinθ|+2sinθ=0

⇒sinθ<0

Therefore, θ will be lying in the third or fourth quadrant.

So, the given assertion is true. 

Reason given:- sin2θ=sinθ 

∵ x2=a2⇒x=±a

So, the given reason is false. 

Asked in: AP EAMCET 2019 (21 Apr Shift 2)

Practice more Trigonometric Equations questions on Aicharya