Trigonometric identities.

  • Thread starter hibernator
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  • #1

Homework Statement



prove that sin^4theta + cos^4 theta =1/4 (3+cos4theta).hence,find the greatest and least value of sin^4theta + cos^4 theta.

please give hints to start . no idea at all...i start from the RHS and get 2cos^4 theta - 2 cos^2 theta +1 , then how sin^4theta + cos^4 theta



Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
eumyang
Homework Helper
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Homework Statement



prove that sin^4theta + cos^4 theta =1/4 (3+cos4theta).hence,find the greatest and least value of sin^4theta + cos^4 theta.

please give hints to start . no idea at all...i start from the RHS and get 2cos^4 theta - 2 cos^2 theta +1 , then how sin^4theta + cos^4 theta

So you started at the RHS and got to this:
2cos4 θ - 2cos2 θ + 1.
You're really close, then. Split the 2cos4 θ and rearrange the terms like so:
cos4 θ + 1 - 2cos2 θ + cos4 θ
Factor the part in bold.
 
Last edited:
  • #3
Amazing idea that i never thought before !! TQ so much eumyang..
 

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