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Q.

If $cosθ = \frac{12}{13}$ and $θ$ is acute, what is the value of $cosecθ$ ?

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a

\frac{12}{5}

b

\frac{5}{13}

c

\frac{13}{5}

d

\frac{11}{5}

answer is C.

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Detailed Solution

Given that

cosθ = \frac{12}{13}

and

θ

is acute.
We know the trigonometric identity

\sin^{2} θ + \cos^{2} θ = 1

.
It is given that,

cosθ = \frac{12}{13}

.
Substitute the given value of

cosθ

in the trigonometric identity mentioned above.
Therefore,

{(\frac{12}{13})}^{2} + \sin^{2} θ = 1

\sin^{2} θ = 1 - \frac{144}{169} = \frac{25}{169}

By adding square root on both the sides, we get

sinθ = \sqrt{\frac{25}{169}} = \frac{5}{13}

Now we know the value of

sinθ

. So, we can find the value of cosec

θ

by just taking the reciprocal.
Therefore,

cosecθ = \frac{13}{5}

.
Hence, the correct option is (3).

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