First slide

Trigonometric equations

Question

If $\sin â¡ Î±, \sin â¡ Î²$ are the roots of the equation $a \sin^{2} â¡ Î¸ + b \sin â¡ Î¸ + c = 0 and \sin â¡ Î± + 2 \sin â¡ Î² = 1$ and $a^{2} + 2 b^{2} + 3 a b + a c =$

Moderate

A

â 1
B

0
C

1
D

$a + b + c$

Solution

$\sin â¡ Î± + \sin â¡ Î² = â b / a, \sin â¡ Î± \sin â¡ Î² = c / a$ , $\sin â¡ Î± + 2 \sin â¡ Î² = 1$
$â \sin â¡ Î± = \frac{c}{a + b}$ which satisfies the given equation
$(Note c â 0)$ and the required value is 0.

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