Question

prove that sin a . sin 2a .sin 4a = 1/4 sin 3a

Answer 1

Answer:

this equation is not true

Step-by-step explanation:

sinA.sin2A.sin4A = (1/4)sin3A

this equation is not true

Let say A = 30°

SinA = Sin30° = 1/2

Sn2A = Sin60° = √3 /2

Sin4A = Sin120° = √3 /2

LHS = (1/2)(√3 /2)(√3 /2) = 3/8

Sin(3A) = Sin90° = 1

RHS = 1/4

=> LHS ≠ RHS

Another example A = 45°

SinA = Sin45° = 1/√2

Sn2A = Sin90° = 1

Sin4A = Sin180° = 0

LHS = 0

Sin(3A) = Sin135° =  1/√2

RHS = 1/4√2

=> LHS ≠ RHS

Another example A = 90°

SinA = Sin90° = 1

Sn2A = Sin180° = 0

Sin4A = Sin360° = 0

LHS = 0

Sin(3A) = Sin270° = -1

RHS = -1/4

=> LHS ≠ RHS