Question

Prove this

1-tan^2x/1+tan^2x=cos^2x-sin^2x

Answer 1

see explanation

Explanation:

Using the identity

tan x =
`(sinx)/(cosx)`

Consider the left side

`(1-tan^2x)/(1+tan^2x)`

=
`(1-(sin^2x)/(cos^2x) )/(1+(sin^2x)/(cos^2x) )` ( multiply numerator and denominator by cos²x to clear fractions

=
`(cos^2x-sin^2x)/(cos^2x+sin^2x)` ← ( cos²x + sin²x = 1 ]

= cos²x - sin²x

= right side , thus proven