Cambridge International AS and A Level 9709-22 - Edubirdie

University:
University of Cambridge
Course:
0580 IGCSE | Mathematics
Academic year:

2023
Views:

390

Pages:

3
Author:

Shahbaz A.

Cambridge International AS and A Level 9709-22 February-March 2023 shahbaz ahmed July 2024 Q 2 Solve the equation tan(θ − 60◦ ) = 3 cot θ for −90◦ < θ < 90◦ Solution tan(θ − 60◦ ) = 3 cot θ f or − 90◦ < θ < 90◦ using the formula tan (A − B) = tan A − tan B 1 + tan A tan B Putting A=θ,B=60◦ tan θ − tan 60◦ tan (θ − 60 ) = 1 + tan θ tan 60◦ ◦ 1 √ tan θ − 3 √ tan (θ − 60◦ ) = 1 + 3 tan θ Putting in tan(θ − 60◦ ) = 3 cot θ f or − 90◦ < θ < 90◦ √ tan θ − 3 √ = 3 cot θ 1 + 3 tan θ f or − 90◦ < θ < 90◦ √ tan θ − 3 1 √ =3 tan θ 1 + 3 tan θ f or − 90◦ < θ < 90◦ tan2 θ − tan2 θ − √ √ √ 3 tan θ = 3 + 3 3 tan θ √ 3 tan θ − 3 3 tan θ − 3 = 0 √ tan2 θ − 4 3 tan θ − 3 = 0 √ 4 3±6 tan θ = 2 √ tan θ = 2 3 ± 3 2 √ θ = arctan (2 3 ± 3) θ = 81◦ 12′ 21.68′ θ = 24◦ 53′ 45.93′′ 3

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