Can I get some help tonight please? Thanks!

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1 Answer
Jim G.
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"#

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