Question

Can you prove `costheta = sectheta-sinthetatantheta`?

Answer 1

Yes, I can.

Explanation:

We ahve `sec(theta)=1/cos(theta)` and `tan(theta)=sin(theta)/cos(theta)`.
I substitute:

`cos(theta)=1/cos(theta)-sin(theta)sin(theta)/cos(theta)`

`cos(theta)=(1-sin(theta)^2)/cos(theta)`

`cos(theta)^2=1-sin(theta)^2`

`cos(theta)^2+sin(theta)^2=1`

That is the fundamental identity of trigonometry.