Question

express sin4A/sinA in terms of cos^3A and cosA

Answer 1

Answer:

Trigonometric function of sin 3A in terms of sin A is also known as one of the double angle formula.

If A is a number or angle then we have, sin 3A = 3 sin A - 4 sin^3 A.

Now we will proof the above multiple angle formula step-by-step.

Proof: sin 3A

= sin (2A + A)

= sin 2A cos A + cos 2A sin A

= 2 sin A cos A ∙ cos A + (1 - 2 sin^2 A) sin A

= 2 sin A (1 - sin^2 A) + sin A - 2 sin^3 A

= 2 sin A - 2 sin^3 A + sin A - 2 sin^3 A

= 3 sin A - 4 sin^3 A

Therefore, sin 3A = 3 sin A - 4 sin^3 A Proved