C3 2017 4 Edexcel

a) R\cos\alpha=5 and R\sin\alpha=2
R=\sqrt{29}
\alpha=0.380506...=0.381 to 3d.p

\therefore 5cos\theta-2sin\theta=\sqrt{29}cos(\theta+0.381)

b) 5cot2x-3cosec2x=2
\Rightarrow \frac{5}{\tan2x}-\frac{3}{\sin2x}=2
\Rightarrow \frac{5\sin2x}{\tan2x}-3=2\sin2x
\Rightarrow 5\cos2x-2\sin2x=3

c) this if the same as finding the solutions to the equation
5\cos2x-2\sin2x=3

from a) we have \sqrt{29}cos(2x+0.381)=3
2x+0.381=0.9799 and 5.3033
\therefore x=0.30 and 2.46

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