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if sintheta+sin^2 theta + sin^3theta =1 then P.T. COS^6THETA -4cos^4theta+8cos^2theta = 4

if sintheta+sin^2 theta + sin^3theta =1 then P.T.
COS^6THETA -4cos^4theta+8cos^2theta = 4

Grade:10

1 Answers

Arun
25763 Points
4 years ago
given, sin\theta+ sin2\theta+ sin3\theta= 1
squaring both the sides-
sin2\theta+sin4\theta+sin6\theta+ 2(sin3\theta+sin4\theta+sin5\theta) = 1
now using identity
(1−cos2\theta)+ (1−cos2\theta)2+ (1−cos2\theta)3+ 2(1−cos2\theta)(sin\theta+ sin2\theta+ sin3\theta)
now if we expand all the formulas,
we will get
cos6\theta− 4cos4\theta+ 8cos2\theta = 4
Hence proved

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