Answer: The value of [Tex]\frac{1}{cos x}[/Tex]​ is equal to sec x, where sec x represents the secant function.

To find the value of [Tex]\bold{\frac{1}{cos x}}[/Tex]​, we use the reciprocal trigonometric function known as the secant function, denoted as sec x. The secant of an angle x is defined as the reciprocal of the cosine of that angle:

sec x = [Tex]\bold{\frac{1}{cos x}}[/Tex]

Therefore, [Tex]\bold{\frac{1}{cos x}}[/Tex]​ is equivalent to sec x. This relationship is derived from the fundamental trigonometric identity sec x = [Tex]\bold{\frac{1}{cos x}}[/Tex].

The secant function has practical applications in trigonometry, physics, and engineering. It represents the ratio of the hypotenuse to the adjacent side in a right-angled triangle and is a fundamental trigonometric function that is used in various mathematical and scientific contexts. Understanding these trigonometric relationships is essential for solving problems involving angles and sides in trigonometry.

Conclusion:

The value of 1/cos(x) is equal to sec(x), where sec(x) represents the secant function. The secant of an angle x is defined as the reciprocal of the cosine of that angle, which is expressed as sec(x) = 1/cos(x). Therefore, 1/cos(x) is equivalent to sec(x), a fundamental trigonometric relationship derived from the secant function’s definition.

Some Related Questions:

How is the secant function related to the cosine function?

The secant function is the reciprocal of the cosine function. In mathematical terms, sec(x) = 1/cos(x). This relationship illustrates the connection between the secant and cosine functions in trigonometry.

Are there any other reciprocal trigonometric functions similar to secant?

Yes, besides secant, there are other reciprocal trigonometric functions such as cosecant (csc) and cotangent (cot). These functions represent the reciprocals of the sine and tangent functions, respectively, and are also fundamental in trigonometry.

Related Articles:

• What is 1-cosx Equal To?
• What is 1+cosx
• Cosine Function: Definition, Graph, Formula, Table