First slide

Multiple and sub- multiple Angles

Question

If $\sin (θ / 2) = a, \cos (θ / 2) = b,$ then $(1 + \sin θ) / (3 \sin θ + 4 \cos θ + 5) =$

Moderate

A

${(a + b)}^{2} / {(a + 3 b)}^{2}$
B

${(a + b)}^{2} / {(3 a + b)}^{2}$
C

${(a - b)}^{2} / {(a + 3 b)}^{2}$
D

${(a - b)}^{2} / {(3 a - b)}^{2}$

Solution

$\tan θ / 2 = a / b,$ write $\sin θ$ and $\cos θ$ in term of $\tan θ / 2$

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