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

Last updated at April 16, 2024 by Teachoo

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.

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, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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