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Mathematics

If 3θ is an acute angle, solve the following equation for θ :

(cosec 3θ - 2)(cot 2θ - 1) = 0.

Trigonometrical Ratios

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Answer

Given,

⇒ (cosec 3θ – 2)(cot 2θ – 1) = 0

⇒ cosec 3θ – 2 = 0 or cot 2θ – 1 = 0

⇒ cosec 3θ = 2 or cot 2θ = 1

⇒ cosec 3θ = cosec 30° or cot 2θ = cot 45°

⇒ 3θ = 30° or 2θ = 45°

⇒ θ = 30°3\dfrac{30°}{3} or θ = 45°2\dfrac{45°}{2}

⇒ θ = 10° or θ = 2212°22\dfrac{1}{2}°

Hence, θ = 10° or θ = 2212°22\dfrac{1}{2}°.

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