Posted by **mo** on Wednesday, April 18, 2007 at 1:26pm.

( tanx/1-cotx )+ (cotx/1-tanx)= (1+secxcscx)

Good one!

Generally these are done by changing everything to sines and cosines, unless you see some obvious identities.

Also generally, it is best to start with the more complicated side and try to change it to the "easier" side.

so here goes....

LS=

sinx/cosx ÷ (1-cosx/sinx) + cosx/sinx ÷(1-sinx/cosx)

=sinx/cosx [sinx/(sinx-cosx) + cosx/sinx [cosx/(cosx-sinx)

=sin^2 x/(cosx(sinx-cosx)) - cos^2 x/(sinx(sinx-cosx))

= (sin^3x - cos^3 x)/(sinxcosx(sinx-cosx))

=(sinx-cosx)(sin^2x + sinxcosx + cos^2)÷[sinxcosx(sinx-cosx)] difference of cubes!!!

= (sin^2x + cos^2x + sinxcosx)/(sinxcosx)

= (1 + sinxcosx)/sinxcosx

R.S.= 1+ 1/(sinxcosx)

=(sinxcosx + 1)/(sinxcosx) = L.S

Wow!!

=

thank you very much for your help .

## Answer this Question

## Related Questions

- Math - 1)A piano tuner uses a tuning fork. If middle C has a frequency of 264 ...
- Pre-calc - prove the identity: (cosx)(tanx + sinx cotx)=sinx+cos(squared)x i ...
- math - solve each identity algebraically 1)(1-tanx)/(1-cotx)=-tanx 2)(1+cotx)/(1...
- Pre-Calc - How do I solve this? My work has led me to a dead end. tan(45-x) + ...
- trigonometry - tanx-cotx/tanx+cotx=1-2cos squardx
- Math (Trigonometry) - We are working on verifing identities using trigonomic ...
- Math - Im really struggling with these proving identities problems can somebody ...
- trig - Verify the trigonometric identity. Please show all steps. tanx-cotx/tanx+...
- trig - verify the identity (tanx+cotx) (1) __________ = ______________ (tanx-...
- matj - prove that (cotx+tanx)(cotx-tanx) = 1/(sin^2 x) - 1/(cos^x)