Trigonometrical question?

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if α, β and γ are three angles of a triangle then

sin2α + sin2β + sin2γ = 4 sinα sinβ sinγ

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  • Sergio
    Lv 5
    2 months ago
    Favorite Answer

    γ = 180 - ( α + β ) ..... 2γ = 360 - ( 2α + 2β )

    you start with these 2 sustitutions

    then formulas  prostaferesis  and  sum/difference of angles

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    • Sergio2 months agoReport

      A good explanation 

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  • Vaman
    Lv 7
    2 months ago

    4 sin a sin b sinc= 2 sin c(sina sinb)= sin c ( cos (a-b)-cos(a+b))= sin (c) cos (a-b) - sin(c) cos (a+b)=( sin (c+a-b)+sin(c-a+b)-(sin(c+a+b)+sin(c-a-b)

    now put the values. = (sin (pi-2b)+sin(pi-2a)+ sin pi+sin(2c-pi)=sin 2b+sin 2a+sin 2c. you expand sin terms and put values. you got the answer.

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