Qus: If tan 4θ=cot(θ−10°), where 4θ and(θ−10°) are acute angles then the value of θ in degrees is

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A. 16°
B. 20°
C. 32°
D. 40°

Solution

B. 20°

Explanation

Given, tan 4θ=cot(θ−10°)

This can be written as

cot(90°− 4θ)=cot(θ−10°) —–(i)

(∵ Tan θ = Cot(90°− θ))

Hence, from (i) we have

⇒90°− 4θ= θ−10°

⇒5θ =100°

⇒θ =20°