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

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  1. Class 10
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Transcript

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
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.