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Prove the identity: [sin x + sin 2x]/[1 + cos x + cos 2x] = tan x

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Best answer

Let us consider the LHS

[sin x + sin 2x]/[1 + cos x + cos 2x]

As we know that, cos 2x = cos2 x – sin2 x

Sin 2x = 2 sin x cos x

Therefore,

= tan x

= RHS

Thus proved.

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