Question

How do i prove 2sec^2x-2sec^2xsin^2-sin^2x-cos^2x=1

Answer 1

`2\sec^2x-2\sec^2x\sin^2x-\sin^2x-\cos^2x=2\sec^2x(1-\sin^2x)-(\sin^2x+\cos^2x)`

Since
`\sin^2x+\cos^2x=1`, you have


`2\sec^2x(1-\sin^2x)-(\sin^2x+\cos^2x)=2\sec^2x\cos^2x-1`

and since
`\sec x=\frac1{\cos x}`, you end up with
`2-1=1`.