If θ be an acute angle and tanθ + cotθ = 2, then the value of 2 tan2θ+ cot2θ + tan4θcot4θ is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 4.
tan θ + cot θ = 2
⇒ tan θ + (1/tan θ) = 2
⇒ tan2θ - 2 tan θ + 1 = 0
⇒ (tan θ - 1)2 = 0
⇒ tan θ - 1 = 0
⇒ tan θ = 1 = tan 45°
⇒ θ = 45°
Now, 2 tan2θ+ cot2θ + tan4θcot4θ
= 2(1)2 + (1)2 + (1)4(1)4
= 2 + 1 + 1
= 4