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If sin πœƒ + cos πœƒ =√3, then prove that tan πœƒ + cot πœƒ = 1

If sin πœƒ + cos πœƒ = √3, then prove that tan πœƒ + cot πœƒ = 1 - Teachoo

Question 32 (OR 1st question) - CBSE Class 10 Sample Paper for 2020 Boards - Maths Standard - Part 2
Question 32 (OR 1st question) - CBSE Class 10 Sample Paper for 2020 Boards - Maths Standard - Part 3

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Question 32 (OR 1st question) If sin πœƒ + cos πœƒ =√3, then prove that tan πœƒ + cot πœƒ = 1 sin πœƒ + cos πœƒ =√3 Squaring both sides (sin πœƒ + cos πœƒ)2 = (√3)^2 (sin πœƒ + cos πœƒ)2 = 3 sin2 πœƒ + cos2 πœƒ + 2 cos ΞΈ sin ΞΈ = 3 Putting sin2 πœƒ + cos2 πœƒ = 1 1 + 2 cos ΞΈ sin ΞΈ = 3 2 cos ΞΈ sin ΞΈ = 3 – 1 2 cos ΞΈ sin ΞΈ = 2 cos ΞΈ sin ΞΈ = 1 We have to prove tan πœƒ + cot πœƒ = 1 Solving LHS tan πœƒ + cot πœƒ = sinβ‘πœƒ/cosβ‘πœƒ +cosβ‘πœƒ/sinβ‘πœƒ = (sin^2β‘πœƒ + cos^2β‘πœƒ)/(cosβ‘πœƒ sinβ‘πœƒ ) Putting sin2 πœƒ + cos2 πœƒ = 1 = 1/(cosβ‘πœƒ sinβ‘πœƒ ) From (1): cos ΞΈ sin ΞΈ = 1 = 1/1 = 1 = RHS Since LHS = RHS Hecne proved

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.