Question

How do you simplify \[\sec x.\cos x\] ?

Answer 1

Hint: we can see that the above expression has a trigonometric function along with its reciprocal. That is when the reciprocal is multiplied by its original function the answer will be 1 only. Thus let’s use this general information and solve the expression above.

Complete step by step answer:
Given that,
\[\sec x.\cos x\]
As we know that sec is the reciprocal of cos function. Thus we will replace the term with the reciprocal itself
That is,
\[\cos x = \dfrac{1}{{\sec x}}\]
Now we will replace the term,
\[ = \sec x.\dfrac{1}{{\sec x}}\]
Since two same terms are placed in the product with its reciprocal term we can cancel them directly.
\[\sec x.\cos x = 1\]
Thus this is the simplified answer.

Note:
Note that, the main three trigonometric functions have their reciprocals as other three trigonometric functions. As sin has cosec as reciprocal, cos has sec as reciprocal and tan has cot as reciprocal. Thus when we come across these types of expressions having trigonometric function and its reciprocal we can use the method above.