Reciprocal of cosine of an angle.

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Tangent

Sine

Cosine

Secant

answer is D.

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Detailed Solution

We have to find the reciprocal of cosine of an angle.
In a right-angled triangle, the cosine θ is given as the ratio between the adjacent and the hypotenuse.
Diagram

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Diagram

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cosθ = \frac{adjacent}{hypotenuse}

Taking the reciprocal,

\frac{1}{cosθ} = \frac{1}{\frac{adjacent}{hypotenuse}}

\frac{1}{cosθ} = \frac{hypotenuse}{Adjacent}

Now,

secθ = \frac{hypotenuse}{adjacent}

So,

\frac{1}{cosθ} = secθ

Thus, the reciprocal of cos θ is sec θ.
Hence, option 4 is correct.

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