How do you verify (tan(x)/(1 + sec(x))) + (1+sec(x)/tan(x)) = 2csc(x)?

1 Answer
Apr 16, 2016

See below

Explanation:

LHS=left hand side, RHS=right hand side

LHS=(tanx)/(1+secx) +(1+secx)/tanx

=((tanx)(tanx)+(1+secx)(1+secx))/(tanx(1+secx))

=(tan^2x+1+2secx+sec^2x)/(tanx(1+secx))

=((tan^2x+1)+2secx+sec^2x)/(tanx(1+secx))

=(sec^2x +2secx+sec^2x)/(tanx (1+secx))

=(2sec^2x+2secx)/(tanx(1+secx))

=(2secx(secx+1))/(tanx(1+secx))

=2 secx/tanx

=2 (1/cosx)/(sinx/cosx)

=2 1/cosx xx cosx/sinx

=2 1/sinx

=2cscx

=RHS