What is the value of cot (90º + 75º)?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. -2 - √3.
cot (90° + 75°)
= - tan 75°
= - tan(45° + 30°)
= -(tan 45° + tan 30°)/(1 - tan 45° tan 30°)
= -[(√3 + 1)/(√3 - 1)]
Rationalising,
= -[(√3 + 1)(√3 + 1)/(√3 - 1)(√3 + 1)]
= -[4 + 2√3]/2
= -2 - √3