Question

Solve this trig identity
(tan-1) (sec-1) =0

Answer 1

I know sec is 1/cos
But I don't think it will help.

Answer 2

Could I square both sides and use the identity that sec^2 -1 =tan?

Answer 3

\[(\frac{\sin x}{\cos x} -1) ( \frac{1}{\cos x}-1)\]

Answer 4

Then cross multiply?

Answer 5

You can use the FOIL method, or take LCM and solve each parenthesis first.

Answer 6

Ok, can you show me how to foil it. I attempted it.

Answer 7

\[\frac{\sin x }{\cos x \times \cos x} - \frac{sinx x}{\cos x} - \frac{1}{\cos x} + 1\]

Answer 8

This will lead you to:
\[\Large \frac{\sin x}{\cos^2 x} - \frac{\sin x-1}{\cos x} + 1\]