AP EAMCET201921 Apr 2019Evening ShiftMathematicsTrigonometric EquationsActual
Assertion ( A ) : If 4 sin 4 θ + sin 2 2 θ + 4 cos 2 π 4 - θ 2 = 2 , then θ lies in 3 rd quadrant or 4 th quadrant. Reason R : sin 2 θ = sin θ
Options
- ABoth ( A ) and ( R ) are true and ( R ) is the correct explanation of ( A )
- BBoth ( A ) and ( R ) are true but ( R ) is not the correct explanation of ( A )
- C( A ) is true but ( R ) is false
- D( A ) is false but ( R ) is true
Correct answer
C. ( A ) is true but ( R ) is false
Step-by-step solution
Assertion given:- 4 sin 4 θ + sin 2 2 θ + 4 cos 2 π 2 - θ 2 = 2 Simplify the above expression. 4 sin 4 θ + 4 sin 2 θ cos 2 θ + 2 1 + cos 2 π 2 - θ 2 = 2 ⇒ 4 sin 2 θ sin 2 θ + cos 2 θ + 2 1 + sin θ = 2 ⇒ 4 sin 2 θ + 2 + 2 sin θ = 2 ⇒ | 2 sin θ | + 2 sin θ = 0 ⇒ sin θ < 0 Therefore, θ will be lying in the third or fourth quadrant. So, the given assertion is true. Reason given:- sin 2 θ = sin