Question 17 (OR 1 st question)

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

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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

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.