Question

16sin(20°) sin(40°) sin(80°) is equal to :  

(A)√3 

(B)2√3 

(C) 3 

(D) 4√3

Answer 1

Correct option is (B) 2√3

16 sin20° sin 40° sin 80° 

= 16 sin 40° sin 20° sin 80° 

= 4(4 sin (60 – 20) sin (20) sin (60 + 20)) 

= 4 × sin (3 × 20°) 

[\(\therefore\) sin 3θ = 4 sin(60 –θ) × sin θ × sin (60 + θ)] 

= 4 × sin 60°

 = 4 x √3/2 = 2√3