Simplify and write the trigonometric expression in terms of

Simplify and write the trigonometric expression in terms of sine and cosine: 2 + tan^2 x/sec^2 x - 1 = g(x) g(x) =

Solution

g(x)=[(1+tan²x)/(sec²x)] -1

write tanx as sinx/cosx , secx as 1/cosx

g(x)=[(1+(sinx/cosx)²)/((1/cosx)²)] -1

g(x)=[(1+(sin²x/cos²x))/(1/cos²x)] -1

g(x)=[(cos²x+sin²x)/cos²x)/(1/cos²x)] -1

g(x)=(cos²x+sin²x) -1