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Chapter 5: Problem 41

Use the fundamental identities to simplify the expression. There is more than one correct form of each answer. $$\cos \left(\frac{\pi}{2}-x\right) \sec x$$

Short Answer

Expert verified
The simplified form of the expression is \( \tan(x) \).

Step by step solution

01

Apply Co-function Identity

Substitute the co-function identity \( \cos(\frac{\pi}{2}-x) = \sin(x) \) into the expression. The new expression becomes \( \sin(x) \sec(x) \).
02

Substitute Reciprocal Identity

Further, we replace \( \sec(x) \) with its reciprocal identity \( \frac{1}{\cos(x)} \). The expression now becomes \( \sin(x) \cdot \frac{1}{\cos(x)} = \frac{\sin(x)}{\cos(x)} \).
03

Get the Final Answer

The final form, \( \frac{\sin(x)}{\cos(x)} \), is equivalent to the identity \( \tan(x) \), hence the expression simplifies to \( \tan(x) \).

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