Question

The value of cot⁻17+cot⁻18+cot⁻118 is

• A. \(\pi\)
• B. \(\dfrac{\pi}{2}\)
• C. \(\cot^{-1}5\)
• D. cot⁻13

Hint:

Use the identity for sum of inverse cotangents to simplify stepwise.

Answer 1

The Correct Option is D

Using cot⁻1a+cot⁻1b=cot⁻1((ab-1)/(a+b)), cot⁻17+cot⁻18=cot⁻1((56-1)/(15))=cot⁻1((11)/(3)). Now, cot⁻1((11)/(3))+cot⁻118 =cot⁻1((66-1)/((11)/(3)+18)) =cot⁻13.