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Ex 3.3, 3 - Prove that cot2 pi/6 + cosec 5pi/6 + 3 tan2 pi/6 = 6

Ex 3.3, 3 - Chapter 3 Class 11 Trigonometric Functions - Part 2
Ex 3.3, 3 - Chapter 3 Class 11 Trigonometric Functions - Part 3

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Ex 3.3, 3 Prove that cot2 π/6 + cosec 5π/6 + 3 tan2 π/6 = 6 Taking L.H.S. cot2 π/6 + cosec 5π/6 + 3 tan2 π/6 Putting π = 180° = cot2(180/6) + cosec((5 ×180)/6) + 3 tan2(180/6) = cot2 30° + cosec (150°) + 3tan2 30° Here, tan 30° = 1/√3 cot 30° = 1/tan⁡〖30°〗 = 1/(1/√3) = √3 For cosec 150° , First, Finding sin 150° sin 150° = sin (180 – 30° ) = sin 30° = 1/2 cosec 150° = 1/sin⁡〖150°〗 = 1/(1/2) = 2 Putting values = cot2 30° + cosec (150°) + 3tan2 30° = (√3)2 + 2 + 3 × (1/√3)^2 = 3 + 2 + 3 × 1/3 = 3 + 2 + 1 = 6 = R.H.S Hence 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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.