Can I get some help tonight please? Thanks!

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1 Answer
Sep 23, 2017

"see explanation"

Explanation:

"using the "color(blue)"trigonometric identities"

•color(white)(x)sin^2theta+cos^2theta=1larrcolor(blue)"Pythagorean identity"

•color(white)(x)cos^2theta/sin^2theta=cot^2theta" and "csc^2theta=1/sin^2theta

"beginning with the Pythagorean identity"

sin^2theta+cos^2theta=1

"divide all terms by "sin^2theta

sin^2theta/sin^2theta+cos^2theta/sin^2theta=1/sin^2theta

rArr1+cot^2theta=csc^2theta

color(blue)"OR"

"left side "=1+cot^2theta=1+cos^2theta/sin^2theta

rArr1+cos^2theta/sin^2theta=(sin^2theta+cos^2theta)/sin^2theta

=1/sin^2theta=csctheta="right side "rArr"verified"