Learn All Concepts of Chapter 2 Class 11 Relations and Function - FREE. Check - Trigonometry Class 11 - All Concepts

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  1. Chapter 3 Class 11 Trigonometric Functions
  2. Serial order wise

Transcript

Example 25 If sin ๐‘ฅ = 3/5 , cos y = โˆ’12/13 , where ๐‘ฅ and y both lie in second quadrant, find the value of sin (๐‘ฅ + y). We know that sin (x + y) = sin x cos y + cos x sin y We know that value of sin x and cos y but we do not know of cos x and sin y Let us first find cos x We know that sin2x + cos2x = 1 (3/5)^2+ cos2x = 1 9/25 + cos2x = 1 9/25 + cos2x = 1 cos2x = 1 โ€“ 9/25 cos2x = (25 โˆ’ 9)/25 cos2x = 16/25 cos x = ยฑ โˆš(16/25) cos x = ยฑ 4/5 Since x is in llnd Quadrant cos x is negative So, cos x = (โˆ’๐Ÿ’)/๐Ÿ“ Similarly, Finding sin y We know that sin2 y + cos2 y = 1 sin2 y = 1 โ€“ cos2 y sin2 y = 1 โ€“ ((โˆ’12)/13)^2 sin2 y = 1 โ€“ 144/169 ("Given cos y =" (โˆ’12)/13) sin2 y = (169 โˆ’ 144)/169 sin2 y = 25/169 sin y = ยฑ โˆš(25/169) sin y = ยฑ โˆš((5 ร— 5)/(13 ร—13)) sin y = ยฑ 5/13 sin y = ยฑ 5/13 Since y lies in llnd Quadrant So, sin y is positive โˆด sin y = 5/13 Now, Putting value of sin x , sin y, cos x, cos y in sin (x + y) = sin x cos y + cos x sin y = 3/5 ร— ((โˆ’12)/13) + ((โˆ’4)/5) (5/13) = (โˆ’12 ร— 3)/(5 ร— 13) + ((โˆ’4 ร— 5)/(5 ร— 13)) = (โˆ’36)/65 + ((โˆ’20)/65) = (โˆ’36 โˆ’20)/65 = (โˆ’56)/65 Hence, sin (x + y) = (โˆ’๐Ÿ“๐Ÿ”)/๐Ÿ”๐Ÿ“

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.