Question

it is known that sin2θ=2sinθcosθ
prove show that sin4θ=sinθcosθcos2θ

Answer 1

you want \[sin(4\theta)=4sin(\theta)cos(\theta)cos(2\theta)\]

Answer 2

sin4θ=sinθcosθcos2θ ??? looks this is not an identity

Answer 3

have u typed correctly ?

Answer 4

sorry there's a typo it should be sin(4θ)=4sin(θ)cos(θ)cos(2θ)

Answer 5

That is \[sin(4\theta)=2sin(2\theta)cos(2\theta)=4sin(\theta)cos(\theta)cos(2\theta)\]

Answer 6

sin2θ=2sinθcosθ (known)
sin4θ = sin2(2θ) = 2sin2θcos2θ
sin4θ = 2(2sinθcosθ)cos2θ
sin4θ = 4sinθcosθcos2θ

Answer 7

thank you!