Simplify and write the trigonometric expression in terms of sine and cosine.

Question

Simplify and write the trigonometric expression in terms of sine and cosine.

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

find g(x)=

Answer 1

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

g(x) = 1 +sin^2x/cos^2x/1/cos^2x = 1 + sin^2(x)

g(x) = 1 + sin^2(x)

unless, by chance, you left out some parentheses and meant to write 2 +tan^2x/(sec^2x -1) = 2 + tan^2/tan^2 = 2+1 = 3

then

g(x) = 3