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Ex 8.3
Ex 8.3, 2 Important
Ex 8.3, 3 (i) [MCQ]
Ex 8.3, 3 (ii) [MCQ] Important
Ex 8.3, 3 (iii) [MCQ] Important
Ex 8.3, 3 (iv) [MCQ]
Ex 8.3, 4 (i) Important
Ex 8.3, 4 (ii) You are here
Ex 8.3, 4 (iii) Important
Ex 8.3, 4 (iv) Important
Ex 8.3, 4 (v) Important
Ex 8.3, 4 (vi)
Ex 8.3, 4 (vii) Important
Ex 8.3, 4 (viii)
Ex 8.3, 4 (ix) Important
Ex 8.3, 4 (x)
Question 1 (i) Important Deleted for CBSE Board 2024 Exams
Question 1 (ii) Deleted for CBSE Board 2024 Exams
Last updated at Aug. 16, 2023 by Teachoo
Ex 8.3, 4 Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (ii) "cos A" /"1 + sin A" +"1 + sin A" /"cos A" =2 sec A Taking L.H.S (cos 𝐴)/(1 + sin〖 𝐴〗 )+(1 + sin 𝐴)/(cos 𝐴) = (cos 𝐴 (cos 𝐴) + (1 + sin 𝐴)(1 + sin〖 𝐴)〗)/((1 + sin 𝐴)(cos 𝐴)) = (𝒄𝒐𝒔𝟐𝑨 + (𝟏 + 𝐬𝐢𝐧𝑨 )𝟐)/((𝟏 + 𝒔𝒊𝒏 𝑨)(𝒄𝒐𝒔𝑨)) = (𝑐𝑜𝑠2 𝐴 + 1^2 + 𝑠𝑖𝑛2 𝐴 + 2 sin𝐴)/((1 + sin 𝐴)(cos𝐴)) = ((𝒄𝒐𝒔𝟐 𝑨 + 𝒔𝒊𝒏𝟐 𝑨) + 1 + 2 sin 𝐴)/((1 + sin〖 𝐴)(cos 𝐴)〗 ) As cos2 A + sin2 A = 1 = (𝟏 + 1 + 2 sin𝐴)/((1 + sin〖 𝐴)(cos 𝐴)〗 ) = (2 + 2 sin 𝐴)/((1 + sin〖 𝐴)(cos 𝐴)〗 ) = (2(1+ sin 𝐴))/((1 + sin〖 𝐴)(cos 𝐴)〗 ) = 𝟐/(𝒄𝒐𝒔 𝑨) = 2 ×1/cos〖 𝐴〗 = 2 sec A = R.H.S ∴ L.H.S = R.H.S Hence proved