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#