Ex 8.1, 6 - Chapter 8 Class 10 Introduction to Trignometry

Transcript

Ex 8.1, 6 If ∠ A and ∠ B are acute angles such that cos A = cos B, then show that ∠ A = ∠ B. cos A = (𝑠𝑖𝑑𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝐴)/𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 = 𝑨𝑪/𝑨𝑩 Similarly, cos B = (𝑠𝑖𝑑𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝐵)/𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 = 𝑩𝑪/𝑨𝑩 Now, given that cos A = cos B 𝐴𝐶/𝐴𝐵 = 𝐵𝐶/𝐴𝐵 AC = BC We know that in a triangle, angles opposite equal sides are equal ∠B = ∠𝐀 Hence proved.