If cosec θ = √5 and θ is less than 90°, find the value of cot θ - cos θ.

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KnowledgeBoat · Accepted Answer

Let ABC be a right angle triangle with ∠C = θ and ∠B = 90°. By formula, cosec θ = . Substituting values we get : Let AC = k and AB = k. In right angle triangle ABC, ⇒ AC² = AB² + BC² ⇒ (k)² = BC² + k² ⇒ 5k² = BC² + k² ⇒ BC² = 5k² - k² ⇒ BC² = 4k² ⇒ BC = ⇒ BC = 2k. cot θ = = = = cos θ = = = = Hence, cot θ - cos θ =

Mathematics

If cosec θ = √5 and θ is less than 90°, find the value of cot θ - cos θ.

Trigonometrical Ratios

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