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.
Prove the identity
(Sin²xcosx + cos³x) ÷ sinx = cotx
1 answer