Posted by Math Lab
on 6/25/2008, 10:23 am, in reply to "MTH 164"
164.106.201.53
I'm changing the thetas to x's to make it a little easier to see. Your identities are in the back of your book, you'll probably need to look at that to know why things are changing into what they are. We work the more complicated looking side first.
1/2tanx+1/2cotx=csc2x
sinx/(2cosx)+cosx/(2sinx)=csc2x (Quotient Identities)
(sinx/sinx)(sinx/(2cosx))+(cosx/cosx)(cosx/(2sinx))=csc2x (Getting a common denominator of 2sinxcosx)
(sinx)^2/(2sinxcosx)+(cosx)^2/(2sinxcosx)=csc2x
((sinx)^2+cosx)^2)/(2sinxcosx)=csc2x (adding the fractions)
1/(2sinxcosx)=csc2x (Pythagorean Identity)
1/sin2x=csc2x (Double Angle Formula)
csc2x=csc2x (Reciprocal Identity)
Both sides are now equal, so we proved our identity.
Happy Calculating!!!!
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