Find an acute angle θ when cos⁡θ - sin⁡θ/cos⁡θ  + sin⁡θ  = 1+ √3/1 + √3

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Question 25 (Choice 2) Find an acute angle θ when (cos⁡θ − sin⁡θ)/(cos⁡θ + sin⁡θ ) = (1 − √3)/(1 + √3)Given (cos⁡θ − sin⁡θ)/(cos⁡θ + sin⁡θ ) = (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° = (cos⁡θ − sin⁡θ)/(cos⁡θ + sin⁡θ ) = (1 − √3)/ So, the correct answer is (c) √3 = sin⁡〖θ 〗/cos⁡〖θ 〗 tan θ = √𝟑 Since tan 60° = √3 Therefore, θ = 60°

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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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.