" I7"quad " Given that "sin theta+2cos theta=1," then prove that "2sin theta-cos theta=2^(7)

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If sin theta+ sin^(2)theta=1 , then prove that cos^(2) theta+cos^(4) theta=1.

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cos theta-cos3 theta+cos5 theta-cos7 theta=4sin theta sin4 theta cos2 theta

2(cos theta+cos2 theta)+(1+2cos theta)sin2 theta=2sin theta