Find an acute angle θ when cosθ - sinθ/cosθ + sinθ = 1+ √3/1 + √3
CBSE Class 10 Sample Paper for 2023 Boards - Maths Standard
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CBSE Class 10 Sample Paper for 2023 Boards - Maths Standard
Last updated at April 16, 2024 by Teachoo
Question 25 (Choice 2) Find an acute angle θ when (cosθ − sinθ)/(cosθ + sinθ ) = (1 − √3)/(1 + √3)Given (cosθ − sinθ)/(cosθ + sinθ ) = (1 − √3)/(1 + √3) Cross multiplying (1 + √3) (cos θ − sin θ) = (1 − √3) (cos θ + sin θ) 1 (cos θ − sin θ) + √3(cos θ − sin θ) = 1 (cos θ + sin θ) − √3 (cos θ + sin θ) cos θ − sin θ + √3cos θ − √𝟑 sin θ = cos θ + sin θ − √3cos θ − √𝟑sin θ − sin θ + √3cos θ = sin θ − √3cos θ √3cos θ + √3cos θ = sin θ + sin θ 2√𝟑cos θ = 2 sin θ √3cos θ = sin θ √3 = sin〖θ 〗/cos〖θ 〗 tan θ = √3 Since tan 60° = (cosθ − sinθ)/(cosθ + sinθ ) = (1 − √3)/ So, the correct answer is (c) √3 = sin〖θ 〗/cos〖θ 〗 tan θ = √𝟑 Since tan 60° = √3 Therefore, θ = 60°