Question 17 (OR 2 nd question)
Prove that sin θ (1 + tan θ) + cos θ (1 + cot θ) = sec θ + cosec θ
CBSE Class 10 Sample Paper for 2019 Boards
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CBSE Class 10 Sample Paper for 2019 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 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 + sin𝜃/cos𝜃 ) + cos θ (1 + cos𝜃/sin𝜃 ) = sin θ ((cos𝜃 + sin𝜃)/cos𝜃 ) + cos θ ((sin𝜃 + cos𝜃)/sin𝜃 ) Taking cos𝜃 + sin𝜃 common = (cos𝜃 + sin𝜃) (sin𝜃/cos𝜃 +cos𝜃/sin𝜃 ) = (cos𝜃 + sin𝜃) ((sin𝜃 × sin𝜃 + cos𝜃 × cos𝜃)/(cos𝜃 sin𝜃 )) = (cos𝜃 + sin𝜃) ((sin^2𝜃 + cos^2𝜃 )/(cos𝜃 sin𝜃 )) Since sin^2𝜃 + cos^2𝜃 = 1 = (cos𝜃 + sin𝜃) ((1 )/(cos𝜃 sin𝜃 )) = (cos𝜃 )/(cos𝜃 sin𝜃 ) + (sin𝜃 )/(cos𝜃 sin𝜃 ) = (1 )/sin𝜃 + (1 )/cos𝜃 = cosec θ + sec θ = RHS Thus LHS = RHS Hence proved