Question

How do you prove Trig Identity `1+tan^2 (x) = sec^2 (x)`?

Answer 1

Have a look:

Explanation:

We can try using:
`tan(x)=(sin(x))/(cos(x))`
and:
`sec(x)=1/cos(x)`
so you get:
`1+(sin^2(x))/(cos^2(x))=1/cos^2(x)`
rearrnaging:
`(cos^2(x)+sin^2(x))/cancel((cos^2(x)))=1/cancel(cos^2(x))`
so that:
`cos^2(x)+sin^2(x)=1` which is true