How do I cerify the identity tanx sinx + cosx = secx

Question

I do not know how to solve and prove this identity.

 

Answer 1

Remember Sin^2x+Cos^2x = 1

Left hand side identity =

=Tanx Sinx + Cosx

= Sinx/Cosx Sinx + Cosx

= Sin^2x|Cosx + Cosx

= (Sin^2x+Cos^2x)/Cosx

= 1/Cosx

= Secx

= Right hand side identity