Question

How do you prove: `[(sinx/cosx) +(cosx/sinx)] = sinx^2+cosx^2`?

Answer 1

The given identity is false.

Explanation:

Consider `x = pi/4`

`sin(pi/4)/cos(pi/4)+cos(pi/4)/sin(pi/4) = (sqrt(2)/2)/(sqrt(2)/2)+(sqrt(2)/2)/(sqrt(2)/2) = 1+1=2`

but

`sin((pi/4)^2)+cos((pi/4)^2) = sin(pi^2/16)+cos(pi^2/16) ~~1.394`