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

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Ex 8.3, 3 Choose the correct option. Justify your choice. (iv) (1 + 𝑡𝑎𝑛2𝐴)/(1 + 𝑐𝑜𝑡2𝐴) sec2 A (B) –1 (C) cot2 A (D) tan2 A (1 + 𝑡𝑎𝑛2𝐴)/(1 + 𝑐𝑜𝑡2𝐴) = (1 + 𝑠𝑖𝑛2𝐴/( 𝑐𝑜𝑠2 𝐴))/(1 + 𝑐𝑜𝑠2𝐴/(𝑠𝑖𝑛2 𝐴)) = ((𝑐𝑜𝑠2 𝐴 + 𝑠𝑖𝑛2 𝐴)/(𝑐𝑜𝑠2 𝐴))/((𝑠𝑖𝑛2 𝐴 + 𝑐𝑜𝑠2 𝐴)/𝑠𝑖𝑛2𝐴) = (𝑐𝑜𝑠2 𝐴 + 𝑠𝑖𝑛2 𝐴)/(𝑐𝑜𝑠2 𝐴) × (𝑠𝑖𝑛2 𝐴)/(𝑐𝑜𝑠2 𝐴 + 𝑠𝑖𝑛2 𝐴) = 𝟏/(𝒄𝒐𝒔𝟐 𝑨) × (𝒔𝒊𝒏𝟐 𝑨)/𝟏 = (𝑠𝑖𝑛2 𝐴)/(𝑐𝑜𝑠2 𝐴) = ((𝑠𝑖𝑛 𝐴)/(𝑐𝑜𝑠 𝐴))^2 = tan2 A So, the correct answer is (d)

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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