If tanθ + cotθ = 2, and θ is an acute angle, then the value of θ is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 45°.
tanθ + cotθ = 2
⇒ tanθ + (1/tanθ) = 2 [∵ cotθ = 1/tanθ]
⇒ tan2θ + 1 = 2tanθ
⇒ tan2θ - 2tanθ + 1 = 0
⇒ (tanθ - 1)2 = 0
⇒ tanθ = 1 = tan 45° (0° < θ < 90°)
⇒ θ = 45°