If tan θ + cot θ = 2, then what is the value of tan θ - cot θ?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 0.
tan θ + cot θ = 2
⇒ tan θ + (1/tan θ) = 2
⇒ tan2 θ - 2 tan θ + 1 = 0
⇒ (tan θ - 1)2 = 0
⇒ tan θ - 1 = 0
⇒ tan θ = 1
⇒ cot θ = 1/1 = 1
⇒ tan θ - cot θ = 1 - 1 = 0