Prove: (secx+tanx)^3(secx-tanx)^4=1-sinx/cosx

Question

Prove: (secx+tanx)^3(secx-tanx)^4=1-sinx/cosx

 

Please show the steps and prove this by making both sides equivalent to each other.  Also, please include which identities follow with each step! :)

Answer 1

Left side = (secx+tanx)³(secx-tanx)³(secx-tanx)

= [(secx+tanx)(secx-tanx)]³(secx-tanx)

=(sec²x- tan²x)³(1/cosx-sinx/cosx)

=1(1-sinx)/cosx

=(1-sinx)/cosx