Question

The value of cot⁻17+cot⁻18+cot⁻118 is

• A. π
• B. (π)/(2)
• C. cot⁻15
• D. cot⁻13

Hint:

For positive numbers, repeated use of the cot–addition identity simplifies sums quickly.

Answer 1

The Correct Option is D

Using cot⁻1a+cot⁻1b=cot⁻1((ab-1)/(a+b)) (a,b>0) cot⁻17+cot⁻18=cot⁻1((56-1)/(15))=cot⁻1((11)/(3)) Now, cot⁻1((11)/(3))+cot⁻118 =cot⁻1(((11/3)·18-1)/((11/3)+18)) =cot⁻13