Question

is cos^2x(1+tan^2x)=1 a trig identity? Can you explain to me why or why not?

Answer 1

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

Answer 2

yeah thats an important trig identity :

\[ 1+\tan^2 x=1+\frac{\sin^2 x}{\cos^2 x}=\frac{\cos^2 x}{\cos^2 x}+\frac{\sin^2 x}{\cos^2 x}=\frac{\cos^2 x+\sin^2 x}{\cos^2 x}=\frac{1}{\cos^2 x} \]

Answer 3

the only thing is the domain must be restricted. They are not the same when cos(x) = 0