Question

Prove that cos(x) and tan(x) are equal at some point on the interval (0, pi/2). I think the intermediate value theorem is the best way to solve it, but I'm not sure how to prove it.

Answer 1

Maybe this has to go like this but not sure
cos x = tan x
cos x = sin x /cos x
cos^2 x= sin x
1-sin^2 x = sinx
sin^2 x +sin x -1=0
The values of x found from this equation will satisfy the equation cos x =tan x