How do you simplify [(2 + tan^2x) / sec^2x] - 1?

2 Answers
Apr 19, 2018

cos^2x.

Explanation:

Since, sec^2x=1+tan^2x, we have,

[(2+tan^2x)/sec^2x]-1,

=[{(2+tan^2x)-sec^2x}/sec^2x],

=[{2-(sec^2x-tan^2x)}/sec^2x],

=(2-1)/sec^2x,

=1/sec^2x,

=cos^2x.

Apr 19, 2018

cos^2x

Explanation:

"using the "color(blue)"trigonometric identity"

•color(white)(x)1+tan^2x=sec^2x

rArr[(1+1+tan^2x)/sec^2x]-sec^2x/sec^2x

=(1+sec^2x)/sec^2x-sec^2x/sec^2x

=1/sec^2x=cos^2x