If cot θ =7/8, evaluate : (i)((1+sinθ)(1-sinθ))/((1+cosθ)(1-cosθ)) (ii) cot^2 θ

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Let us draw a right angle triangle ABC, with ∠A = θ. We know that, cot θ = Substituting values we get : Let AB = 7k and BC = 8k. In right angle triangle ABC, ⇒ AC² = AB² + BC² ⇒ AC² = (7k)² + (8k)² ⇒ AC² = 49k² + 64k² ⇒ AC² = 113k² ⇒ AC = . (i) We know that, sin θ = . cos θ = . Substituting values of sin θ and cos θ in , we get : Hence, . (ii) Given, ⇒ cot θ = ⇒ cot² θ = . Hence, cot² θ = .

Mathematics

If cot θ =7/8, evaluate : (i)((1+sinθ)(1-sinθ))/((1+cosθ)(1-cosθ)) (ii) cot^2 θ

Trigonometric Identities

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