Question

Verify formula

`sin^2x+tan^2x+cos^2x =sec^2x`
​

Answer 1

L.H.S=R.H.S

Explanation:

L.H.S=sin²x+tan²x+cos²x

=tan²x+1 *** sin²x+cos²x=1 ***

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

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

=
`(1)/(cos^(2)x )`

=sec²x ***
`(1)/(cos^(2)x )`=sec²x***