Question

Sin^3A.cos A + Cos^ 3 A = Cos A​

Answer 1

Answer:

One root is 90 degrees or  π/2 radians.

Drawing a graph we get all the roots:

nπ and π(n - 1/2)

Step-by-step explanation:

Sin^3A.cos A + Cos^ 3 A = Cos A​

Divide through by cos A

sin^3A + cos^2A = 1

sin^3 A = 1 - cos^2 A

sin^3 A = sin^2 A

sin A = 1

So one  root is A = 90 degrees or π/2 radians.

Checking this result:

(sin 90^3 * cos 90 + (cos 90)^3 = 1 * 0 + 0 = 0

cos 90 = 0

So this is correct..