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Ex 8.1, 7 - If cot = 7/8, evaluate (i) (1 + sin) (1 - sin) - Finding values of expressions

Ex 8.1, 7 - Chapter 8 Class 10 Introduction to Trignometry - Part 2
Ex 8.1, 7 - Chapter 8 Class 10 Introduction to Trignometry - Part 3 Ex 8.1, 7 - Chapter 8 Class 10 Introduction to Trignometry - Part 4

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Ex 8.1, 7 - Chapter 8 Class 10 Introduction to Trignometry - Part 5

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Ex 8.1, 7 If cot ΞΈ = 7/8 , evaluate : (i) ((1 + π‘ π‘–π‘›β‘πœƒ)(1 βˆ’ π‘ π‘–π‘›β‘πœƒ))/((1 + π‘π‘œπ‘ β‘πœƒ)(1 βˆ’ π‘π‘œπ‘ β‘πœƒ)) We will first calculate the value of sin ΞΈ & cos ΞΈ Now, tan ΞΈ = 1/cotβ‘πœƒ tan ΞΈ = 1/(7/8) tan ΞΈ = 8/7 (𝑠𝑖𝑑𝑒 π‘œπ‘π‘π‘œπ‘ π‘–π‘‘π‘’ βˆ πœƒ)/(𝑠𝑖𝑑𝑒 π‘Žπ‘‘π‘—π‘Žπ‘π‘’π‘›π‘‘ βˆ πœƒ)=8/7 𝐡𝐢/𝐴𝐡=8/7 Let BC = 8x & AB = 7x We find AC using Pythagoras theorem (Hypotenuse)2 = (Height)2 + (Base)2 AC2 = AB2 + BC2 AC2 = (7x)2 + (8x)2 AC2 = 49x2 + 64x2 AC2 = 113x2 AC = √113π‘₯2 AC = √113 x Now, we need to find sin ΞΈ and cos ΞΈ sin πœƒ = (𝑠𝑖𝑑𝑒 π‘œπ‘π‘π‘œπ‘ π‘–π‘‘π‘’ π‘‘π‘œ βˆ πœƒ)/π»π‘¦π‘π‘œπ‘‘π‘’π‘›π‘’π‘ π‘’ = 𝐡𝐢/𝐴𝐢 = 8π‘₯/(√113 π‘₯) = 8/(√113 ) Here, We have to evaluate ((1 + sinβ‘πœƒ ) (1 βˆ’γ€– sinγ€—β‘πœƒ ))/((1 + cosβ‘πœƒ ) (1 βˆ’γ€– cosγ€—β‘πœƒ ) ) Using (a + b) (a – b) = a2 – b2 = ( (12 βˆ’ 𝑠𝑖𝑛2 πœƒ))/( (12 βˆ’ π‘π‘œπ‘ 2πœƒ)) = ( (1 βˆ’ 𝑠𝑖𝑛2 πœƒ))/( (1 βˆ’ π‘π‘œπ‘ 2πœƒ)) Putting sin πœƒ = 8/(√113 ) & cos ΞΈ = 7/(√113 ) = ((1 βˆ’ (8/(√113 ))^2 ))/((1 βˆ’ (7/(√113 ))^2 ) ) = ((1 βˆ’ 8^2/(√113)2))/((1 βˆ’ 72/(√113)2) ) = ((1 βˆ’ 64/113))/((1 βˆ’ 49/113) ) = (((113 βˆ’ 64)/113))/(((113 βˆ’ 49)/113) ) = (113 βˆ’ 64)/(113 βˆ’ 49 ) = 49/(64 ) Hence, ((1 + π‘ π‘–π‘›β‘πœƒ)(1 βˆ’ π‘ π‘–π‘›β‘πœƒ))/((1 + π‘π‘œπ‘ β‘πœƒ)(1 βˆ’ π‘π‘œπ‘ β‘πœƒ)) = 49/(64 )

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.