anonymous
  • anonymous
Please help*** Proving Trigonometric Identities
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
|dw:1436290113123:dw|
SolomonZelman
  • SolomonZelman
\(\large\color{black}{ \displaystyle 1-2\sin^2\theta=2\cos^2\theta-1 }\)
SolomonZelman
  • SolomonZelman
\(\large\color{black}{ \displaystyle 1-2\sin^2\theta=2\cos^2\theta-1 }\) knowing that \(\large\color{blue}{ \displaystyle 1=\sin^2\theta+\cos^2\theta }\) \(\large\color{black}{ \displaystyle (\sin^2\theta+\cos^2\theta)-2\sin^2\theta=2\cos^2\theta-(\sin^2\theta+\cos^2\theta) }\) \(\large\color{black}{ \displaystyle \sin^2\theta+\cos^2\theta-2\sin^2\theta=2\cos^2\theta-\sin^2\theta-\cos^2\theta }\) now, finish and simplify.

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anonymous
  • anonymous
I'm still lost @SolomonZelman
SolomonZelman
  • SolomonZelman
you can't add/subtract like terms?
anonymous
  • anonymous
would it be sin^2 (theta) + cos^2(theta) = cos^2(theta) - sin^2 (theta) @SolomonZelman
SolomonZelman
  • SolomonZelman
x-2x=?
anonymous
  • anonymous
-x
SolomonZelman
  • SolomonZelman
good
SolomonZelman
  • SolomonZelman
sin²θ - 2sin²θ = ?
anonymous
  • anonymous
-sin^2(theta)
SolomonZelman
  • SolomonZelman
yes
anonymous
  • anonymous
so is it
SolomonZelman
  • SolomonZelman
so, your left side is \(\large\color{black}{ \displaystyle -\sin^2\theta+\cos^2\theta }\) and the right side is \(\large\color{black}{ \displaystyle \cos^2\theta-\sin^2\theta }\) (the right side is same as left side, so yes, it is an identity)
anonymous
  • anonymous
Thanks
SolomonZelman
  • SolomonZelman
yw

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