Ex 8.3, 3 (ii) [MCQ] - Chapter 8 Class 10 Introduction to Trignometry

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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)