Question

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

Answer 1

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

Answer 2

can u ?

Answer 3

where do i use the sin2θ = 2sinθcosθ

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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))

Answer 8

so, LHS = RHS

Answer 9

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?