Question

Find the derivative of the function
(1 - cos 2x)/(1+cos2x)​

Answer 1

Answer ::: 2tanx sec²x

Answer 2

The derivative of (1 - cos 2x)/(1+cos2x)​ is 2tanx.sec²x.

Given,

A function (1 - cos 2x)/(1+cos2x)​

To Find,

The derivative of the given function.

Solution

The given function is

f(x) = (1 - cos 2x)/(1+cos2x)​

Now,

cos2x = 1-2sin²x

2sin²x = 1-cos2x----(i)

Also

2cos²x = 1+cos2x----(ii)

Now, substituting the value from (i) and (ii) in the given function

f(x) = 2sin²x/2cos²x

f(x) = tan²x

Now,

f'(x) = d(tan²x)/dx

using the chain rule

f'(x) = 2tanx.sec²x

Hence, the derivative of (1 - cos 2x)/(1+cos2x)​ is 2tanx.sec²x.

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