Solve the equation $$\(2 \sin \left(\theta+30^{\circ}\right)+5 \cos \theta=2 \sin \theta\)$$ for $$\(0^{\circ}<\theta<90^{\circ}\)$$. ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................

Mathematics
IGCSE&ALevel
CAIE
Exam No:9709_m20_qp_22 Year:2020 Question No:1

Answer:

Express first term as \(2 \sin \theta \cos 30+2 \cos \theta \sin 30\)
Divide by \(\cos \theta\) to produce linear equation in \(\tan \theta\) Obtain \(\tan
\theta=\frac{6}{2-\sqrt{3}}\)
or \(22.39 \ldots\)
Obtain \(87.4\)

Knowledge points:

1.5.4 use the identities
2.3.2.2 the expansions of

Solution:

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