Prove that: (sin x - 2 sin³ x)/(2 cos³ x - cos x) = tan x

We have to prove that:

Taking LHS, we get:

We can take sin(x) as common from numerator part. We get:

Similarly, we can take cos(x) as common from first two terms. We get:

As we know that:

We get:

Now, we will expand the terms in fraction:

As we know that:

Now substitute the values in the expression, we get:

Here, we notice that LHS = RHS

Proved.

step-by-step explanation:

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step-by-step explanation: