First slide

Compound angles

Question

If $\sin θ_{1} - \sin θ_{2} = a and \cos θ_{1} + \cos θ_{2} = b$ then

Moderate

A

$a^{2} + b^{2} \geq 4$
B

$a^{2} + b^{2} \leq 4$
C

$a^{2} + b^{2} \geq 3$
D

$a^{2} + b^{2} \leq 2$

Solution

$\begin{array}{l} \sin θ_{1} - \sin θ_{2} = a, \cos θ_{1} + \cos θ_{2} = b \\ \Rightarrow a^{2} + b^{2} = 2 + 2 \cos (θ_{1} + θ_{2}) \\ \Rightarrow 0 \leq a^{2} + b^{2} \leq 4 \end{array}$

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