Question #84c50

1 Answer
Apr 12, 2017

See below

Explanation:

1+(color(red)(sin^2theta))/(cos^2theta)

Use the following identity to solve for sin^2theta

sin^2theta+cos^2theta=1

sin^2theta=color(red)(1-cos^2theta)

Substitute this instead of sin^2theta

1+(sin^2theta)/(cos^2theta)=1+(color(red)(1-cos^2theta))/cos^2theta

Add 1 and (1-cos^2theta)/cos^2theta together by unifying the denominators (1 is

the same as cos^2theta/cos^2theta), so

color(red)1+(1-cos^2theta)/cos^2theta=color(red)(cos^2theta/cos^2theta)+(1-cos^2theta)/cos^2theta

=(cancel(cos^2theta)+1cancel(-cos^2theta))/cos^2theta

=1/cos^2theta

=sec^2theta