Question

How do you simplify $\dfrac{1}{{\sec x}}$?

Answer 1

In the given question, we have been given an expression. This expression has one trigonometric function – in the denominator. We have to simplify the value of the trigonometric function. We know that all the trigonometric functions can be represented in a combination of sine and cosine and that is how we simplify each trigonometric function, and then combine them both to get a single answer for the whole expression.

Complete step-by-step answer:
The given expression is $p = \dfrac{1}{{\sec x}}$.
Now, we know that:
$\sec x = \dfrac{1}{{\cos x}}$
Hence, $p = \dfrac{1}{{\dfrac{1}{{\cos x}}}}$
Simplifying them,
$p = \dfrac{{\cos x}}{1} = \cos x$
Hence, $\dfrac{1}{{\sec x}} = \cos x$

Additional Information:
We got the answer to this expression containing the two trigonometric functions by substituting the values of the secant as the value of cosine. Perhaps if we want to simplify any expression containing the trigonometric functions, we can use the two basic trigonometric functions of sine and cosine to get to the answer.

Note: In the given question, we had to simplify the value of an expression containing one trigonometric function. We did that by converting $\sec x = \dfrac{1}{{\cos x}}$. To do any kind of simplification of trigonometric functions, we can just simplify them into sine and cosine and then combine them and then solve them. Hence, it is important that we know these basic formulae.