Question

(sec^2x+csc^2x)-(tan^2x+cos^2x) Simplify to one trig function?

Answer 1

`(sec^2x+csc^2x)-(tan^2x+cos^2x)=sin^2x+1/sin^2x=(sin^4x+1)/sin^2x`

Explanation:

`(sec^2x+csc^2x)-(tan^2x+cos^2x)`

= `sec^2x+csc^2x-tan^2x-cos^2x`

= `sec^2x-tan^2x-cos^2x+csc^2x`

= `1-cos^2x+csc^2x`

= `sin^2x+1/sin^2x`

= `(sin^4x+1)/sin^2x`