What is the value of [(tan 5θ + tan 3θ)/{4 cos 4θ(tan 5θ - tan 3θ)}]?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e cos 2θ
[(tan 5θ + tan 3θ)/{4 cos 4θ(tan 5θ - tan 3θ)}]
Put θ = 15°
= [(tan 75° + tan 45°)] / [4 cos 60°(tan 75° - tan 45°)]
= [2 + √3 + 1] / [4 × (1/2)(1 + √3)]
= [3 + √3] / [2(1 + √3)]
= [√3(1 + √3)] / [2(1 + √3)]
= √3/2
Going through option
⇒ Sin 2θ = Sin 30° = 1/2
⇒ Cos 2θ = Cos 30° = √3/2
⇒ Tan 4θ = Tan 60° = √3
⇒ Cot 2θ = Cot 30° = √3