establish the identity sin²θcos²θ = 1/8[1-cos4θ]

Question

establish the identity sin²θcos²θ  = 1/8[1-cos4θ]

raden · Answer

use the these identity  :
sin2θ = 2sinθcosθ and
sin^2 (2θ) = (1-cos(4θ))/2

raden · Answer

can u ?

anonymous · Answer

where do i use the sin2θ = 2sinθcosθ

raden · Answer

from sin2θ = 2sinθcosθ -----> sinθcosθ = sin2θ/2, agree ?

anonymous · Answer

wait? where is the sin2θ coming from is that = to sin^2(θ)

raden · Answer

i just let u to prove from left side
sin²θcos²θ = (sinθcosθ)² = [(sin2θ)/2]² = 1/4 sin^2 (2θ)

raden · Answer

now, we subtitute the identiy sin^2 (2θ) = (1-cos(4θ))/2 to equation above
sin²θcos²θ = 1/4 * (1-cos(4θ))/2 = 1/8 * (1-cos(4θ))

raden · Answer

so, LHS = RHS

anonymous · Answer

wait i am confused. we are supposed to only change the left side to equal the right side. can you show me a step by step to get to that by only changing things on the left?

raden · Answer

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