Question

if A=15°,verify that 4 sin 2A .cos4A sin6A=1

Answer 1

Hey
Here's your answer

A = 15 degree
so 2A = 30 deg.
4A = 60 deg.
6A = 90 deg.
RTP : 4 sin 2A .cos4A sin6A=1.

L.H.S.
4 sin 30 * cos 60 * sin 90
= (4* 1/2)* (1/2) * 1
= 2 *1/2 *1
= 1.
R.H.S. = 1

SO RHS = LHS [PROVED].

☆☆Hope it helps☆☆

Answer 2

Answer:

4 sin 2A×cos4A× sin6A=1 is proved

Step-by-step explanation:

Given,

A=15°

To prove,

4 sin 2A×cos4A× sin6A=1

Recall the values

sin 30° = $\frac{1}{2}$

cos 60° = $\frac{1}{2}$

sin 90° = 1

Solution:

sin 2A = sin 2 ×15 = sin 30°

∴ sin 2A = sin 30

cos 4A = cos  4 ×15 =  cos 60°

∴ cos 4A = cos 60

Sin 6A =  sin 6×15 = sin 90°

∴ sin 6A = sin 90

LHS = 4 sin 2A× cos4A ×sin6A

Substituting the values of sin2A, cos4A, and sin 90 we get

4 sin 2A× cos4A ×sin6A = 4×sin 30°×cos 60°× sin 90°

Substituting the values of sin 30°, cos 60°, sin 90° we get

= 4× $\frac{1}{2}$× $\frac{1}{2}$× 1

= 1 = RHS

∴ 4 sin 2A×cos4A× sin6A=1

Hence proved

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