Question

convert sin6A+sin2A as product​

Answer 1

Step-by-step explanation:

Sin 6A + sin 2A = 2 Sin [(6A+2A)/2] Cos [(6A-2A)/2]

= 2 Sin (8A/2) Cos (4A/2)

= 2 Sin 4A Cos 2 A

Answer 2

Answer:

sin 6A + sin 2A = 2sin4A cos2A

Step-by-step explanation:

Given the trigonometric relation, $sin 6A + sin 2A$

Using the trigonometric identity,

$sinA + sin B=2\big(sin\frac{A+B}{2} \big)\big(cos\frac{A-B}{2} \big)$

Using A = 6A and B = 2A, the given relation can be written as

$sin 6A + sin 2A=2\big(sin\frac{6A+2A}{2} \big)\big(cos\frac{6A-2A}{2} \big)$

$=2\big(sin\frac{A+B}{2} \big)\big(cos\frac{A-B}{2} \big)$

$=2\big(sin\frac{8A}{2} \big)\big(cos\frac{4A}{2} \big)$

$=2sin4A~cos2A$

Therefore, sin 6A + sin 2A = 2sin4A cos2A