By simplifying the left hand side ($LHS$LHS) of the identity, prove that $\frac{1-\cos2x}{\sin2x}=\tan x$1−cos2xsin2x=tanx.

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Approx 6 minutes

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By simplifying the left hand side ($LHS$LHS) of the identity, prove that $\frac{2\tan A}{1+\tan^2\left(A\right)}=\sin2A$2tanA1+tan2(A)=sin2A.

By simplifying the left hand side ($LHS$LHS) of the identity, prove that $\frac{2\sin^3\left(x\right)+2\cos^3\left(x\right)}{\sin x+\cos x}=2-\sin2x$2sin3(x)+2cos3(x)sinx+cosx=2−sin2x, for $\sin x+\cos x\ne0$sinx+cosx≠0.