Question

How do you express `sin^2 theta - sec theta + tan^2 theta` in terms of `cos theta`?

Answer 1

`1/cos^2 theta-1/cos theta-cos^2 theta`

Explanation:

The expression contains three trigonometric functions, `sin^2 theta`, `sec theta` and `tan^ theta`.

In terms of `cos theta`, these are respectively `1-cos^2 theta`, `1/cos theta` and `sec^2 theta-1` i.e. `1/cos^2 theta-1`.

Hence expression `sin^2 theta-sec theta+tan^2 theta` in terms of `cos theta` can be written as

`1-cos^2 theta-1/cos theta+1/cos^2 theta-1` or

`-cos^2 theta-1/cos theta+1/cos^2 theta`

or `1/cos^2 theta-1/cos theta-cos^2 theta`

(transposition done as `1/cos^2 theta` would be the largest term among three.