Help! Trig identities!

We have to verify the identity by baisically showing all the in between process. You have the problem, and you have the solution, its just the how get ther by baisicallt transforming the different parts.

Ex. (tanX-secX)2=1-sinX/1+sinX

starting with the left hand side (because it's easier that way)
walterthewhale
10 November 2011
(tanX-secX)^2 = tan^2X - 2tanXsecX + sec^2X
walterthewhale
10 November 2011
taking out a factor of 1/cos^2X gives
walterthewhale
10 November 2011
= sin^2X/cos^2X - 2(sinX/cos^2X) + 1/cos^2X
walterthewhale
10 November 2011
factorising the first part & using trig substitution on the bottom...
walterthewhale
10 November 2011
(sin^2X - 2sinX +1)(1/cos^2X)
walterthewhale
10 November 2011
factorising the last part...
walterthewhale
10 November 2011
(1 - sinX)(1 - sinX)(1/(1-sin^2X)
walterthewhale
10 November 2011
cancelling common factors on the top & bottom...
walterthewhale
10 November 2011
(1 - sinX)(1 - sinX)(1/((1-sinX)(1+sinX))
walterthewhale
10 November 2011
(1-sinX)/(1+sinX) QED
walterthewhale
10 November 2011
note that sin^2X means sin squared X or (sinX)^2, NOT sin2X which is a different thing entirely, hope this helps
walterthewhale
10 November 2011