Question #a263e

1 Answer
Scott F.
Apr 3, 2017

I'm going to assume you mean cotthetasintheta=(1-sin^2theta)sectheta, correct me if I'm wrong.

Explanation:

Working the right side, first use the Pythagorean identity sin^2theta+cos^2theta=1 to know that 1-sin^2theta=cos^2theta.
(1-sin^2theta)sectheta=cos^2thetasectheta.

Then, substitute 1/costheta for sectheta and simplify.
cos^2thetasectheta=cos^2theta/costheta=costheta.

Then multiply by 1 in the form of sintheta/sintheta.
costheta=(costhetasintheta)/sintheta.

And substitute cottheta for costheta/sintheta.
(costhetasintheta)/sintheta=cotthetasintheta

Therefore, (1-sin^2theta)sectheta=cotthetasintheta
Q.E.D.

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