Question

How do you simplify `(1 + tan^2 x)(cos^2 x)`?

Answer 1

Simplify: (1 + tan^2 x) (cos^2 x)

Ans: 1

Explanation:

`(1 + sin^2 x/cos^2x) cos^2 x = [(cos^2 x + sin^2 x)/cos^2 x]cos^2 x =`

`(sin^2 x + cos^2 x) = 1`

Answer 2

You can use two identities:

`1+tan^2x = sec^2x`
`sec^2x = 1/cos^2x`

Therefore:

`= sec^2x*cos^2x = cos^2x/cos^2x = 1`