How do you simplify the expression #1+tan^2theta#?

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Answer 1 · 2018-07-16T11:36:19

The answer is #=sec^2theta#

We need

#tantheta=sintheta/costheta#

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

#1/costheta=sectheta#

The expression is

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

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

#=1/cos^2theta#

#=sec^2theta#

Answer 2 · 2018-07-16T11:37:36

#1+\tan^2\theta=\sec^2\theta#

#1+\tan^2\theta#

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

#={\cos^2\theta+\sin^2\theta}/\cos^2\theta#

#={1}/\cos^2\theta#

#=\sec^2\theta#