Solve the equation $$\[ \frac{\tan \theta+3 \sin \theta+2}{\tan \theta-3 \sin \theta+1}=2 \]$$ for $$\(0^{\circ} \leqslant \theta \leqslant 90^{\circ}\)$$. ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................
Exam No：9709_m20_qp_12 Year：2020 Question No：5
Answer:
\(2 \tan \theta-6 \sin \theta+2=\tan \theta+3 \sin \theta+2 \rightarrow \tan \theta-9 \sin \theta(=0)\)
\(\sin \theta-9 \sin \theta \cos \theta(=0)\)
\(\sin \theta(1-9 \cos \theta)(=0) \rightarrow \sin \theta=0, \quad \cos \theta=\frac{1}{9}\)
\(\theta=0\) or \(83.6^{\circ}\) (only answers in the given range)
\(\sin \theta-9 \sin \theta \cos \theta(=0)\)
\(\sin \theta(1-9 \cos \theta)(=0) \rightarrow \sin \theta=0, \quad \cos \theta=\frac{1}{9}\)
\(\theta=0\) or \(83.6^{\circ}\) (only answers in the given range)
Knowledge points:
1.1.5 recognise and solve equations in which are quadratic in some function of
1.5.4 use the identities
1.5.5 find all the solutions of simple trigonometrical equations lying in a specified interval (general forms of solution are not included).
Solution:
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