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prove that sin 10*sin 30*sin 50 …

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prove that sin 10*sin 30*sin 50 *sin 70= 1/16

    • Posted by Adarsh Mund 4 years ago

    CBSE > Class 11 > Mathematics
    • 1 answers

    Sameer Tanwar 4 years ago

    We know that i) sin 2A = 2sinAcosA ii) sin(90-A)= cosA iii) sin30=1/2 LHS = sin 10 sin30 sin50sin 70 =sin 10 × 1/2 × sin (90-40)× sin(90-20) =1/2[sin 10 ×cos 40×cos 20] We multiply with[2 cos 10/2cos 10] =(1/2×1/2cos10)[2sin10cos10×cos20×cos40] =(1/4cos10)[sin20cos20×cos40] =(1/8cos10)[2sin20cos20×cos40] =(1/8cos10)[sin40cos40] =(1/16cos10)[2sin40co40] =(1/16cos10)×sin80 =(1/16cos10)×sin(90-10) =(1/16cos10)×cos10 =1/16 = RHS

    2Thank You

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