SOLUTION: Verify the identity sinx(cscx+sinx〖sec〗^2 x)=〖sec〗^2 x

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Question 916596: Verify the identity sinx(cscx+sinx〖sec〗^2 x)=〖sec〗^2 x
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
sin%28x%29%28csc%28x%29%2Bsin%28x%29%2Asec%5E2%28x%29%29=sec%5E2%28x%29
highlight%28sin%28x%29%28csc%28x%29%2Bsin%28x%29%2Asec%5E2%28x%29%29%29 ....prove it's equal to right side

we know that csc%28x%29=1%2Fsin%28x%29
then we have
=sinx%281%2Fsin%28x%29+%2Bsinx%2Asec%5E2+%28x%29%29

=sinx%281%2Fsin%28x%29+%2B%28sin%28x%29%2Asin%28x%29%2Asec%5E2%28x%29%29%2Fsin%28x%29%29

=sin%28x%29%281%2Fsin%28x%29+%2B%28sin%5E2%28x%29%2Asec%5E2%28x%29%29%2Fsin%28x%29%29


=

=1%2Bsin%5E2%28x%29%2Asec%5E2%28x%29......sin%5E2%28x%29%2Asec%5E2%28x%29=tan%5E2%28x%29

=1%2Btan%5E2%28x%29 ....use Pythagorean Identities =>1%2Btan%5E2%28x%29=sec%5E2%28x%29

=highlight%28sec%5E2%28x%29+%29