anonymous
  • anonymous
Verify the identity. Show your work. (1 + tan2u)(1 - sin2u) = 1
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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SolomonZelman
  • SolomonZelman
\(\large\color{black}{ \displaystyle(1+\tan~2u)(1-\sin~2u)=1 }\) Expand the parenthesis, I suppose.
SolomonZelman
  • SolomonZelman
I don't think that it is indeed an identity (\(\forall x\)) to be honest, but ...
anonymous
  • anonymous
@q12157

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anonymous
  • anonymous
Since sin(2u)=2sinucosu and cos2u=1-2sin^2(u), cos2u is also equal to cos^2(u)-sin^2(u) or 2cos^2(u)-1
anonymous
  • anonymous
you use those identities and plug them in...expand and then voila you should get 1 on the left side.
SolomonZelman
  • SolomonZelman
Wait, is it? \(\large\color{black}{ \displaystyle(1+\tan^2u)(1-\sin^2u)=1 }\) I am asking, because THIS would be an indetity as opposed to the first one.
SolomonZelman
  • SolomonZelman
\(\large\color{black}{ \displaystyle(1+\tan^2u)(1-\sin^2u)=1 }\) Some hepful properties: \(\large\color{blue}{ \displaystyle[1]\quad \quad \sec^2\theta =1+\tan^2\theta }\) \(\large\color{blue}{ \displaystyle[2]\quad \quad \cos^2\theta=1-\sin^2\theta }\) \(\large\color{blue}{ \displaystyle[3]\quad \quad 1= \cos\theta \times\sec \theta \quad \Longrightarrow 1=\cos^{\color{red}N}\theta \times\sec^{\color{red}N}\theta}\)

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