Question 17 (Or 2nd) - CBSE Class 10 Sample Paper for 2019 Boards - Solutions of Sample Papers for Class 10 Boards

Last updated at April 16, 2024 by Teachoo

Question 17 (OR 2 nd question)

Prove that sin θ (1 + tan θ) + cos θ (1 + cot θ) = sec θ + cosec θ

Question 17 (Or 2nd) - CBSE Class 10 Sample Paper for 2019 Boards - Part 2

Question 17 (Or 2nd) - CBSE Class 10 Sample Paper for 2019 Boards - Part 3

Transcript

Question 17 (OR 2nd question) Prove that sin θ (1 + tan θ) + cos θ (1 + cot θ) = sec θ + cosec θ Solving LHS sin θ (1 + tan θ) + cos θ (1 + cot θ) = sin θ (1 + sin⁡𝜃/cos⁡𝜃 ) + cos θ (1 + cos⁡𝜃/sin⁡𝜃 ) = sin θ ((cos⁡𝜃 + sin⁡𝜃)/cos⁡𝜃 ) + cos θ ((sin⁡𝜃 + cos⁡𝜃)/sin⁡𝜃 ) Taking cos⁡𝜃 + sin⁡𝜃 common = (cos⁡𝜃 + sin⁡𝜃) (sin⁡𝜃/cos⁡𝜃 +cos⁡𝜃/sin⁡𝜃 ) = (cos⁡𝜃 + sin⁡𝜃) ((sin⁡𝜃 × sin⁡𝜃 + cos⁡𝜃 × cos⁡𝜃)/(cos⁡𝜃 sin⁡𝜃 )) = (cos⁡𝜃 + sin⁡𝜃) ((sin^2⁡𝜃 + cos^2⁡𝜃 )/(cos⁡𝜃 sin⁡𝜃 )) Since sin^2⁡𝜃 + cos^2⁡𝜃 = 1 = (cos⁡𝜃 + sin⁡𝜃) ((1 )/(cos⁡𝜃 sin⁡𝜃 )) = (cos⁡𝜃 )/(cos⁡𝜃 sin⁡𝜃 ) + (sin⁡𝜃 )/(cos⁡𝜃 sin⁡𝜃 ) = (1 )/sin⁡𝜃 + (1 )/cos⁡𝜃 = cosec θ + sec θ = RHS Thus LHS = RHS Hence proved

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Davneet Singh

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.

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