How do you prove (tanx+cotx)/(secx+cscx)=1/(cosx+sinx)?

1 Answer
Mar 9, 2018

See Below

Explanation:

LHS : (tan x+cot x)/(sec x + csc x)

=(sinx/cosx + cosx/sinx)/(1/cosx + 1/sinx)

=((sin^2x+cos^2x)/(sinxcosx))/((sinx+cosx)/(sinxcosx))->common denominator

=(sin^2x+cos^2x)/(sinxcosx) *(sinxcosx)/ (sinx+cosx)

=(sin^2x+cos^2x)/cancel(sinxcosx) *cancel(sinxcosx)/ (sinx+cosx)

=(sin^2x+cos^2x)/(sinx+cosx)->use property sin^2x+cos^2x=1

=1/(sinx+cosx)

=RHS