Q13 of 31 Page 316

If tan 4θ × tan 6θ = 1 and 6θ is a positive acute angle, let us find the value of θ.

Given, 6θ as a positive acute angle


⇒ tan4θ tan6θ = 1


⇒ tan4θ cot(90 - 6θ) = 1


⇒


⇒ cot(90 - 6θ) = cot4θ


⇒ 90 - 6θ = 4θ


⇒ 10θ = 90


⇒ θ = 9


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