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 August 14, 2026 by Teachoo

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

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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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