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Question Number 91038 by  M±th+et+s last updated on 27/Apr/20

if sin((α/2))=(4/5)  and cos((β/2))=(3/5)  prove  sin(α)=cos(β)

ifsin(α2)=45andcos(β2)=35provesin(α)=cos(β)

Commented by jagoll last updated on 27/Apr/20

sin α = 2sin ((α/2))cos ((α/2))  = 2×(4/5)×(3/5) = ((24)/(25))  cos β = 2sin ((β/2))cos ((β/2))  = 2×(3/5)×(4/5)= ((24)/(25))

sinα=2sin(α2)cos(α2)=2×45×35=2425cosβ=2sin(β2)cos(β2)=2×35×45=2425

Answered by $@ty@m123 last updated on 27/Apr/20

sin^2 (α/2)+cos^2 (β/2)=((4^2 +3^2 )/5^2 )  sin^2 (α/2)+cos^2 (β/2)=1  ⇒(α/2)=(β/2)  ⇒α=β

sin2α2+cos2β2=42+3252sin2α2+cos2β2=1α2=β2α=β

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