Simplify to a single trig function with no denominator

Question

asked Feb 22, 2024 136k views

1 Answer

Sanae · Answer 1 · 2024-02-27T10:42:54+0000

Answer:
$9\tan^(2)x$

Explanation:

Recall the following Pythagorean identity:

$\tan^(2)x+1=\sec^(2)x\\\therefore \sec^(2)x-1=\tan^(2)x --(1)$

Then, we simplify the following:

$9\sec^(2)x-9=9(\sec^(2)x-1)--(2)$

Substitute (1) into (2), and we get:

$9\sec^(2)x-9=9\tan^(2)x$