If cos π7, cos 3π7, cos4π7 are the roots of the equation 8x3-4x2-4x+1 = 0
then the What are the values of expressions sinπ14sin3π14sin5π14 and cosπ14cos3π14cos5π14????
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4 Answers
62if sin α = t
then cos 2a = 1-2t2
Which is a root.. of the given cubic equation...
Hence 8(1-2t2)3-4(1-2t2)2-4(1-2t2)+1=0
This gives -64t6 + ..... + 1
Hence the product of all roots is -1/64
of which the roots are t and -t both...
Hence the given product of sin terms is 1/8
(Assuming the post I have given above... )
1oh ...i also did t he same thing , but as soon as the sixth degree equation came , i got perturbed ,didnt realise that if t is root so will be -t :P
using similar logic and replacing x by 2y2-1
we get πcosθ as √78
