Answer:
One root is 90 degrees or π/2 radians.
Drawing a graph we get all the roots:
nπ and π(n - 1/2)
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..