Posted by Hailey on Thursday, April 10, 2008 at 8:43am.
verify the identities:
1.) 2tanx(1+tanx)^2 = secx
2.) cos(x330degrees)=1/2(ã3cosxsinx)
*the ãis only over the 3*
3.)
1+cos2x/sinx=cotx
any help is greatly appreciated!!

Math (Trig) typo edit  Hailey, Thursday, April 10, 2008 at 8:49am
ã is supposed to represent square root.
so for number 2
it's 1/2 (square root 3 cosxsinx)

Math (Trig) a.s.a.p, thanks!  Reiny, Thursday, April 10, 2008 at 11:57am
1.
LS = 2sinx/cosx  (1+sinx/cosx)^2
= 2sinx/cosx  ((cosx + sinx)/cosx)
= 2sinx/cosx  (cos^2 x + 2sinxcosx + sin^2 x)/cos^2 x
= (2sinxcosx (1 + 2sinxcosx))/cos^2 x
= 1/cos^2 x
= sec^2 x
you had secx on the right side
I think you made a typo
2. LS = cosxcos330 + sinxsin330
but sin 330 = sin30 = 1/2
and cos 330 = cos30 = √3/2
so above
= (√3/2)cosx  1/2 sinx
= 1/2(√3 cosx  sinx)
= RS
Why don't you try the third one.
Change everything to sines and cosines
let me know how you did.

Math (Trig) a.s.a.p, thanks!  Reiny, Thursday, April 10, 2008 at 12:07pm
for the third one you had
1+cos2x/sinx=cotx
Your lack of brackets made this ambiguous.
I tried (1+cos2x)/sinx=cotx and tested with 40º, did not work
I tried 1+cos^2 x/sinx=cotx and tested with 40º, did not work
I tried 1+(cos2x/sinx)=cotx and tested with 40º, did not work
check your typing of the question.
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