Question

Let A = 30°. Verify that

sin 3A = 3 sin A - 4 $Sin^{3}$ A

Answer 1

Hey !!



A = 30°




3A = 3 × 30 = 90°


Sin3A = 3 Sin A - 4 × Sin³





LHS = Sin 3A = Sin90° = 1


And,


RHS = 3 Sin A - 4 Sin³ A



=> 3 Sin30° - 4 Sin³ 30°



=> [ 3 × 1/2 - 4 × (1/2)³ ]




=> ( 3/2 - 4 × 1/8 )



=> ( 3/2 - 1/2 )



=> 1


Hence,


LHS = RHS = 1

Answer 2

Solution :

Given That A = 30°

To prove : Sin 3A = 3 Sin A - 4 Sin³ A

Proof :

LHS : -

Sin 3A

Substituting value of A

Sin ( 3 * 30 ) = Sin 90 = 1

RHS : -

3 Sin A - 4 Sin³ A

Substituting value of A

3 * Sin 30° - 4 * Sin³ 30

= 3 * $\frac{1}{2}$ - 4 * $(\frac{1}{2}) ^{3}$

= 3/2 - 1/2

= 2/2

= 1

Therefore LHS = RHS , i.e. Sin 3A = 3 Sin A - 4 Sin³ A = 1

Hence Proved !!!