cot(π/4 - 2 cot^-1 3) = A. 4 B. 6 C. 5 D. none of these

Question

cot(\(\frac \pi4\) - 2 cot^-13) =

A. 4

B. 6

C. 5

D. none of these

Answer 1

Correct answer is D. none of these

We need to find the value of

cot(\(\frac \pi4\) - 2 cot^-13)

Let 2 cot^-13 = y

Then,

cot^-13 = \(\frac{y}2\)

⇒ cot\(\frac{y}2\) = 3

Substituting 2 cot^-1 3 = y,

Put the value of cot\(\frac y2\) = 3 derived above and also cot² \(\frac y2\) = 3² = 9.