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Trigonometric Ratios of Compound Angles

fx= sin x and...

Question

$f (x) = sin x$ and $g (x) = sec x$ then $\frac{f (π) - f (\frac{3 π}{2}) + f (0)}{g (π) + g (0) + g (\frac{π}{3})}$

A

\frac{1}{2}

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B

1

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C

2

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D

\frac{1}{3}

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Solution

The correct option is A $\frac{1}{2}$
$f (π) = 0; f (\frac{3 π}{2}) = - 1; f (0) = 0$
$g (π) = - 1; g (0) = 1; g (\frac{π}{3}) = 2$
$∴ \frac{f (π) - f (\frac{3 π}{2}) + f (0)}{g (π) + g (0) + g (\frac{π}{3})}$ $= \frac{1}{2}$

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