Question #788a3

2 Answers
May 24, 2017

By derivation.
Start with #cos^2(x)+sin^2(x)=1#
Divide both sides by #cos^2(x)#
The result is: #1 + sin^2(x)/cos^2(x) = 1/cos^2(x)#
This the same as the given equation.

May 24, 2017

Use trig properties.

Explanation:

We know that:

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

We also know that:

#sectheta=1/costheta#

Transforming the second property listed, we get:

#sectheta=1/costheta#
#(sectheta)^2=(1/costheta)^2#

Then applying the first property:

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

#QED#