Question

How do you simplify `[(2 + tan^2x) / sec^2x] - 1`?

Answer 1

`cos^2x`.

Explanation:

Since, `sec^2x=1+tan^2x`, we have,

`[(2+tan^2x)/sec^2x]-1`,

`=[{(2+tan^2x)-sec^2x}/sec^2x]`,

`=[{2-(sec^2x-tan^2x)}/sec^2x]`,

`=(2-1)/sec^2x`,

`=1/sec^2x`,

`=cos^2x`.

Answer 2

`cos^2x`

Explanation:

`"using the "color(blue)"trigonometric identity"`

`•color(white)(x)1+tan^2x=sec^2x`

`rArr[(1+1+tan^2x)/sec^2x]-sec^2x/sec^2x`

`=(1+sec^2x)/sec^2x-sec^2x/sec^2x`

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