Hello everyone,

I am trying to prove the following trigonometric identity, but I am not getting the answer given by my textbook:

Could somoene please comment on my work?

Thank you very much.

*This question actually comes from my attempt to integrate

, where

. I arrived at the LHS of (*) and am trying to get the RHS.

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**My work:**

.

1. The last expression doesn't match the textbook's given answer.

2. Also, could someone please justify the removal of the absolute value sign for the second term on the RHS

?

I know that

so I can remove the absolute sign for this term, but

is both negative and positive on this interval.