Mark the Correct alternative in the following:

The value of is

Given to find the value of

We will solve the expression in two parts,

Now solving 1^st term

If we multiply and divide the term by 2, we get,

[using the formula for and ]

----- (1)

Solving the 2^nd term

[using the formula for ]

1 – 2 tan x cot 2x = 1 – ( 1 – tan²x)

= 1 – 1 + tan²x

1 – 2 tan x cot 2x = tan² x ----- (2)

Now by combining (1) and (2) we get,

Hence the answer is option D.