34. sin 10°. sin 30°. sin 50°. sin 70°. sin 90º =
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Answer:
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
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