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Question 17 (Or 1st) - CBSE Class 10 Sample Paper for 2019 Boards - Solutions of Sample Papers for Class 10 Boards

Last updated at Dec. 16, 2024 by Teachoo

Question 17 (OR 1 st question)

Prove that cot ⁡θ - tan ⁡θ = (2 cos 2 ⁡θ  - 1) / (sin⁡ θ cos ⁡θ)

Transcript

Question 17 (OR 1st question) Prove that cot⁡𝜃−tan⁡𝜃 = (2 cos^2⁡𝜃 − 1)/(sin⁡𝜃 cos⁡𝜃 ) Solving LHS cot⁡𝜃−tan⁡𝜃 = cos⁡𝜃/sin⁡𝜃 −sin⁡𝜃/cos⁡𝜃 = (cos⁡𝜃 × cos⁡𝜃 − sin⁡𝜃 × sin⁡𝜃)/(sin⁡𝜃 cos⁡𝜃 ) = (cos^2⁡𝜃 − sin^2⁡𝜃)/(sin⁡𝜃 cos⁡𝜃 ) Now, sin2 θ + cos2 θ = 1 sin2 θ = 1 – cos2 θ = (cos^2⁡𝜃 − (1 − cos^2⁡𝜃))/(sin⁡𝜃 cos⁡𝜃 ) = (cos^2⁡𝜃 − 1 + cos^2⁡𝜃)/(sin⁡𝜃 cos⁡𝜃 ) = (2 cos^2⁡𝜃 − 1)/(sin⁡𝜃 cos⁡𝜃 ) = RHS Since LHS = RHS Hence proved
  1. Class 10
  2. Solutions of Sample Papers for Class 10 Boards

    3. CBSE Class 10 Sample Paper for 2019 Boards

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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 and Computer Science at Teachoo