Question

If 4sin^ϴ -1=0 and ϴ is an acute angle , then evaluate
(a) cos 2ϴ
(b) sin 3ϴ

Answer 1

Hey friend,

4sin² ∅ -1=0
4sin² ∅ = 1 (by bringing 1 on right side)
sin² ∅=1/4. (by dividing both sides with 4)
sin ∅=√1/4.
sin ∅=1/2 (by finding square root on both sides)
sin ∅=sin 30°
∅ = 30°

(a)tan²∅+cos²∅=(1/√3)²+(√3/2)²=1/3+3/4=13/12

(b)cos 2∅ = cos 2*30°=cos 60°=1/2

(c)sin 3∅= sin 3*30°=sin 90°=1

#hope it helps.....