![part 2 - Ex 8.3, 3 (iv) [MCQ] - Ex 8.3 - Serial order wise - Chapter 8 Class 10 Introduction to Trignometry](https://cdn.teachoo.com/882d86fa-9b76-40b3-b11a-2f1322a12540/slide14.jpg)
Ex 8.3
Last updated at Dec. 16, 2024 by Teachoo
Transcript
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)