Question

(cos x)^2 (tan x)^2 -1 …divided by… (cos x)^2

Simplify.

Answer 1

Answer:

(Secx)^2 -2

Step-by-step explanation:

{(Cosx)^2 (tanx)^2 -1}/ (cosx)^2

{(Sinx)^2 -1}/ (cosx)^2

(Cosx)^2/(cosx)^2

1

Answer 2

$\bf \textit{Pythagorean Identities} \\\\ sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta )=1-sin^2(\theta ) \\\\[-0.35em] ~\dotfill\\\\ \cfrac{[cos(x)]^2[tan(x)]^2-1}{[cos(x)]^2}\implies \cfrac{cos^2(x)tan^2(x)-1}{cos^2(x)}\implies \cfrac{cos^2(x)\frac{sin^2(x)}{cos^2(x)}-1}{cos^2(x)} \\\\\\ \cfrac{sin^2(x)-1}{cos^2(x)}\implies \cfrac{-[1-sin^2(x)]}{cos^2(x)}\implies \cfrac{-cos^2(x)}{cos^2(x)}\implies -1$