Trig Identities
posted by Donovan .
Please help...I'm not understanding trig identities and how to manipulate and express these two problems in their associated functions.
Thanks
a)Express as a function of cos (theta)
2 sin^2(theta)  1
b)Express as a function of sin (theta) or cos (theta)
tan^2(theta)  2 sec(theta)sin(theta)

I will use x instead of theta for easier typing
2 sin^2 x  1 = cos 2x
do you have to prove this?
if so, then
RS = cos(2x)
= cos(x+x)
= cosxcosx + sinxsinx
= cos^x + sin^x
= (1sin^x_ + sin^x
= 2sin^x  1
= LS 
for the second
tan^x  2secxsinx
= sin^2 x/cos^2 x  2sinx/cosx
= sin^2 x/cos^2 x 2 sinxcosx/cos^2 x
= (sin^2 x  sin 2x)/(1  sin^2 x)
this is in terms of sinx
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