If tanθ + cotθ = 2, θ is an acute angle, then find the value of 2 tan25 θ + 3 cot20 θ + 5 tan30 θ cot15 θ.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 10.
Given that
If tanθ + cotθ = 2,
When we put θ = 45º, satisfies the equation
the value of 2 tan25 θ + 3 cot20 θ + 5 tan30 θ cot15 θ
⇒ 2 tan25 θ + 3 cot20 θ + 5 tan30 θ cot15 θ
⇒ 2 tan25 45º + 3 cot20 45º+ 5 tan30 45º cot15 45º
⇒ 2 × 1 + 3 × 1 + 5 × 1 × 1
⇒ 2 + 3 + 5
⇒ 10