SOLUTION: Prove sin^2x/cosx + secx = sinx/cotx + 1/cosx is an identity.

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Question 1201964: Prove sin^2x/cosx + secx = sinx/cotx + 1/cosx is an identity.
Found 2 solutions by math_tutor2020, mananth:
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!
We could transform the LHS (left hand side) so that it becomes the RHS (right hand side).
I'll keep the RHS the same throughout each step.













This confirms the original equation is an identity.

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Or we could alter the RHS to transform it into the LHS.

This time the LHS stays the same for each step.













We get the same thing on both sides, which confirms the equation is an identity.

Here is a list of common identities
https://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf
For example, one common identity I used was sec%28x%29+=+1%2Fcos%28x%29. That example is mentioned under the "Reciprocal Identities" section.

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
sin^2x/cosx + secx = sinx/cotx + 1/cosx is an identity.
+%28sinx%2Fcosx%29%2Asinx+%2B%281%2Fcosx%29
tanx%2Asinx%2B%281%2Fcosx%29........ because sinx / cosx = tanx
%28sinx%2Fcotx%29+%2B%281%2Fcosx%29........ tanx = 1/cotx