Prove the identity

(Sin²xcosx + cos³x) ÷ sinx = cotx

1 answer

Starting with the left side of the equation:

(Sin²x * cosx + cos³x) ÷ sinx

Using the identity sin²x = 1 - cos²x, we can rewrite the left side as:

((1 - cos²x) * cosx + cos³x) ÷ sinx

Expanding the expression:

(cosx - cos³x + cos³x) ÷ sinx

Canceling out the middle terms:

cosx ÷ sinx

Using the identity cotx = cosx / sinx, we can further simplify the expression:

cotx

Therefore, the left side of the equation simplifies to cotx, which matches the right side of the equation. Hence, the identity is proven.