If θ is an acute angle and tanθ + cotθ = 2, then the value of tan2θ + cot2θ + 2 tan5θcot4θ is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 4.
We know that, tanθ + cotθ = 2 when θ = 45°
Hence, tan 45 = 1 and cot 45 = 1
⇒ tan245 + cot245 + 2 tan545.cot445
⇒ 1 + 1 + 2 × 1 × 1 = 4