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Ex 8.3, 3 Choose the correct option. Justify your choice. (ii) (1 + tan θ + sec θ) (1 + cot θ – cosec θ) (A) 0 (B) 1 (C) 2 (D) –1 (1 + tan θ + sec θ) (1 + cot θ – cosec θ) Writing in terms of sin θ & cos θ = (1+" " sin⁡𝜃/cos⁡𝜃 " + " 1/cos⁡𝜃 " " ) (1+" " cos⁡𝜃/sin⁡𝜃 " − " 1/sin⁡𝜃 " " ) = ((cos⁡𝜃 + sin⁡𝜃 + 1))/cos⁡𝜃 × ((sin⁡𝜃 + cos⁡𝜃 − 1))/sin⁡𝜃 = (({𝐜𝐨𝐬⁡𝜽 + 𝐬𝐢𝐧⁡𝜽 } + 𝟏) ({𝐬𝐢𝐧⁡𝜽 +𝐜𝐨𝐬⁡𝜽 } − 𝟏))/(cos⁡𝜃 sin⁡𝜃 ) = ( (cos⁡𝜃 + sin⁡𝜃 )2 − 12)/(cos⁡𝜃 sin⁡𝜃 ) = (𝒄𝒐𝒔𝟐 𝜽 + 𝒔𝒊𝒏𝟐 𝜽 + 2 cos⁡𝜃 sin⁡𝜃 − 1)/(cos⁡𝜃 sin⁡𝜃 ) As cos2 A + sin2 A = 1 = (𝟏 + 2 cos⁡𝜃 sin⁡𝜃 − 1)/(cos⁡𝜃 sin⁡𝜃 ) = (2 cos⁡𝜃 sin⁡𝜃)/(cos⁡𝜃 sin⁡𝜃 ) = 2 So, the correct answer is (c)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo