How can you verify the identity cos^2x+sinxtanx=secx

Question

This is a question i have had a problem with for a while now. How can I solve it?

Answer 1

Multiply through by cosx: cos^3x+sin^2x=1; cos^3x+1-cos^2x=1; cos^3x-cos^2x=0; cos^2x(cosx-1)=0. Therefore, cosx=1 or cosx=0 so x=0 or 90 ((pi)/2). The value x=90 makes secx and tanx incalculable, so x=0 is the only solution. But this is a specific values, not a general value, therefore the original equation is not an identity but an equation with specific solutions.