CBSE Class 10 Sample Paper for 2020 Boards - Maths Standard

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Question 32 (OR 1st question) - CBSE Class 10 Sample Paper for 2020 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at April 16, 2024 by

If sin 𝜃 + cos 𝜃 =√3, then prove that tan 𝜃 + cot 𝜃 = 1

If sin 𝜃 + cos 𝜃 = √3, then prove that tan 𝜃 + cot 𝜃 = 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

Transcript

Question 32 (OR 1st question) If sin 𝜃 + cos 𝜃 =√3, then prove that tan 𝜃 + cot 𝜃 = 1 sin 𝜃 + cos 𝜃 =√3 Squaring both sides (sin 𝜃 + cos 𝜃)2 = (√3)^2 (sin 𝜃 + cos 𝜃)2 = 3 sin2 𝜃 + cos2 𝜃 + 2 cos θ sin θ = 3 Putting sin2 𝜃 + cos2 𝜃 = 1 1 + 2 cos θ sin θ = 3 2 cos θ sin θ = 3 – 1 2 cos θ sin θ = 2 cos θ sin θ = 1 We have to prove tan 𝜃 + cot 𝜃 = 1 Solving LHS tan 𝜃 + cot 𝜃 = sin⁡𝜃/cos⁡𝜃 +cos⁡𝜃/sin⁡𝜃 = (sin^2⁡𝜃 + cos^2⁡𝜃)/(cos⁡𝜃 sin⁡𝜃 ) Putting sin2 𝜃 + cos2 𝜃 = 1 = 1/(cos⁡𝜃 sin⁡𝜃 ) From (1): cos θ sin θ = 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 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.