Ex 8.1

Chapter 8 Class 10 Introduction to Trignometry
Serial order wise

### Transcript

Ex 8.1, 7 If cot ฮธ = 7/8 , evaluate : (i) ((1 + ๐ ๐๐โก๐)(1 โ ๐ ๐๐โก๐))/((1 + ๐๐๐ โก๐)(1 โ ๐๐๐ โก๐)) We will first calculate the value of sin ฮธ & cos ฮธ Now, tan ฮธ = 1/cotโก๐ tan ๐ = ๐/๐ We can write tan ๐ = 8/7 (๐๐๐๐ ๐๐๐๐๐๐๐๐ โ ๐ฝ)/(๐๐๐๐ ๐๐๐๐๐๐๐๐ โ ๐ฝ)=๐/๐ ๐ต๐ถ/๐ด๐ต=8/7 Let BC = 8x & AB = 7x We find AC using Pythagoras Theorem In right triangle ABC Using Pythagoras theorem Hypotenuse2 = Height2 + Base2 AC2 = AB2 + BC2 AC2 = (7x)2 + (8x)2 AC2 = 49x2 + 64x2 AC2 = 113x2 AC = โ113๐ฅ2 AC = โ๐๐๐ x AC = โ๐๐๐ x Now, we need to find sin ฮธ and cos ฮธ sin ๐ฝ = (๐ ๐๐๐ ๐๐๐๐๐ ๐๐ก๐ ๐ก๐ โ ๐)/๐ป๐ฆ๐๐๐ก๐๐๐ข๐ ๐ = ๐ต๐ถ/๐ด๐ถ = 8๐ฅ/(โ113 ๐ฅ) = ๐/(โ๐๐๐ ) cos ๐ฝ = (๐ ๐๐๐ ๐๐๐๐๐๐๐๐ก ๐ก๐ โ ๐)/๐ป๐ฆ๐๐๐ก๐๐๐ข๐ ๐ = ๐ด๐ต/๐ด๐ถ = 7๐ฅ/(โ113 ๐ฅ) = ๐/(โ๐๐๐ ) We have to find ((๐ + ๐ฌ๐ข๐งโก๐ฝ ) (๐ โใ ๐ฌ๐ข๐งใโก๐ฝ ))/((๐ + ๐๐จ๐ฌโก๐ฝ ) (๐ โใ ๐๐จ๐ฌใโก๐ฝ ) ) Using (a + b) (a โ b) = a2 โ b2 = ( (12 โ ๐ ๐๐2 ๐))/( (12 โ ๐๐๐ 2๐)) = ( (1 โ ๐ ๐๐2 ๐))/( (1 โ ๐๐๐ 2๐)) Putting sin ๐ฝ = ๐/(โ๐๐๐ ) & cos ฮธ = ๐/(โ๐๐๐ ) = ((1 โ (8/(โ113 ))^2 ))/((1 โ (7/(โ113 ))^2 ) ) = ((๐ โ ๐๐/๐๐๐))/((๐ โ ๐๐/๐๐๐) ) = (((113 โ 64)/113))/(((113 โ 49)/113) ) = (113 โ 64)/(113 โ 49 ) = ๐๐/(๐๐ ) Hence, ((๐ + ๐๐๐โก๐ฝ)(๐ โ ๐๐๐โก๐ฝ))/((๐ + ๐๐๐โก๐ฝ)(๐ โ ๐๐๐โก๐ฝ)) = ๐๐/(๐๐ ) Ex 8.1, 7 If cot ฮธ = 7/8 , evaluate : (ii) cot2 ฮธ Given cot ฮธ = 7/8 So, cot2 ฮธ = (7/8)^2 = 72/82 = ๐๐/๐๐