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How are secant and cosine related?

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Diagram of a right triangle labeled with sides a, b, and hypotenuse c, alongside formulas for the six trigonometric functions-sine, cosine, tangent, cosecant, secant, and cotangent-each defined by ratios of the triangle's sides. — trigonometry Based on the definitions, various simple relationships exist among the functions. For example, csc A = 1/sin A, sec A = 1/cos A, cot A = 1/tan A, and tan A = sin A/cos A.

In trigonometry, the secant and cosine functions are reciprocals of each other. This relationship is defined by the following equations:

$\frac{1}{\sec A} = \cos A$ 1
$\frac{1}{\cos A} = \sec A$ 2

In a right triangle, the cosine of an angle $A$ is defined as the ratio of the length of the side adjacent to the angle to the length of the hypotenuse. Conversely, the secant of angle $A$ is defined as the ratio of the length of the hypotenuse to the length of the side adjacent to the angle.12