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# How do you simplify $\sec \left( x \right)\cos \left( x \right)$?

Last updated date: 20th Jun 2024
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Hint: In the given question, we have been given an expression. This expression has two trigonometric functions being multiplied. We have to simplify the value of the trigonometric functions as a whole in the expression. We know that all the trigonometric functions can be represented in a combination of sine and cosine and that is how we will simplify each of the trigonometric functions, and then combine them both to get a single answer for the whole expression.

Complete step by step solution:
The given expression is $p = \sec \left( x \right)\cos \left( x \right)$.
Now, we know that:
$\sec \left( x \right) = \dfrac{1}{{\cos \left( x \right)}}$
Hence, $p = \dfrac{1}{{\not{{\cos \left( x \right)}}}} \times \not{{\cos \left( x \right)}} = 1$

Thus, $\sec \left( x \right)\cos \left( x \right) = 1$