The discussion focuses on proving the identity sin4θ + cos4θ = 1/4 (3 + cos 4θ) and finding its maximum and minimum values. Participants suggest starting from the right-hand side (RHS) and manipulating the expression to facilitate the proof. A key insight involves rearranging terms to factor the expression effectively, leading to a clearer path toward the solution. The collaborative nature of the discussion highlights the importance of peer assistance in tackling complex mathematical proofs.
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hibernator said: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