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3 years ago

Sin^3A.cos A + Cos^ 3 A = Cos A

Mathematics

1 answer:

MissTica3 years ago

6 0

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..

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4 years ago

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4 years ago

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4 years ago

Sin^3A.cos A + Cos^ 3 A = Cos A​

Sin^3A.cos A + Cos^ 3 A = Cos A