Ex 3.3, 9 - Chapter 3 Class 11 Trigonometric Functions
Last updated at Dec. 13, 2024 by Teachoo
Last updated at Dec. 13, 2024 by Teachoo
Ex 3.3, 9 Prove cos (3Ο/2+π₯) cos (2Ο + π₯)[cot (3Ο/2βπ₯) + cot (2Ο + π₯)] =1 Solving L.H.S. Now, cos (ππ /π "+ " π) = sin x cos (2Ο + x) = cos x cot (2Ο + x) = cot x cot (ππ /πβπ) = tan x Now putting values in equation cos (3Ο/2+π₯) cos (2Ο + π₯)[cot (3Ο/2βπ₯) + cot (2Ο + π₯)] = (sin x) Γ (cos x) Γ [tan x + cot x] = (sin x cos x) Γ [cot x + tan x] = (sin x cos x) Γ [πππβ‘π/πππβ‘π + πππβ‘π/πππβ‘π ] = (sin x cos x) Γ [(γ(cosγβ‘π₯) Γ γ(cosγβ‘π₯)+γ (sinγβ‘π₯) Γ γ(sinγβ‘π₯))/(sinβ‘π₯ Γ γ(cosγβ‘π₯))] = (sin x cos x) Γ [(ππ¨π¬πβ‘π +γ π¬π’π§πγβ‘π)/(πππβ‘π Γ γ(πππγβ‘π))] = cos2β‘π₯ +γ sin2γβ‘π₯ = 1 = R.H.S Hence proved
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