How do you verify (tan(x)/(1 + sec(x))) + (1+sec(x)/tan(x)) = 2csc(x)(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 =tanx1+secx+1+secxtanx

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

=(tan^2x+1+2secx+sec^2x)/(tanx(1+secx))=tan2x+1+2secx+sec2xtanx(1+secx)

=((tan^2x+1)+2secx+sec^2x)/(tanx(1+secx))=(tan2x+1)+2secx+sec2xtanx(1+secx)

=(sec^2x +2secx+sec^2x)/(tanx (1+secx))=sec2x+2secx+sec2xtanx(1+secx)

=(2sec^2x+2secx)/(tanx(1+secx))=2sec2x+2secxtanx(1+secx)

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

=2 secx/tanx=2secxtanx

=2 (1/cosx)/(sinx/cosx)=21cosxsinxcosx

=2 1/cosx xx cosx/sinx=21cosx×cosxsinx

=2 1/sinx=21sinx

=2cscx=2cscx

=RHS=RHS