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Prove that (sin x-2sin^3 x)/(2cos^3x -cos x)=tan x

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SOLUTION: We have,

$\ LHS=sinx-2sin^3x/2cos^3x-cosx \ \Rightarrow LHS=sinx(1-2sin^2x)/cosx(2cos^2x-1)\ \Rightarrow LHS=sinx/cosx=tanx$

$\ Rightarrow cos2x=1-2sin^2x=2cos^2x-1$

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Deependra Verma

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