Question

Question #788a3

Answer 1

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.

Answer 2

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`