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Chapter 5: Problem 34

Verify the identity. $$\frac{\cos [(\pi / 2)-x]}{\sin [(\pi / 2)-x]}=\tan x$$

Short Answer

Expert verified
The given trigonometric identity \(\frac{\cos[\pi / 2-x]}{\sin[\pi / 2-x]}=\tan x\) is verified

Step by step solution

01

Rewrite using Trigonometric Identities

Replace \(\cos\left(\frac{\pi}{2} - x\right)\) with \(\sin(x)\) and \(\sin\left(\frac{\pi}{2} - x\right)\) with \(\cos(x)\). This gives: \(\frac{\sin(x)}{\cos(x)}\)
02

Recognize the Resultant Expression

The expression \(\frac{\sin(x)}{\cos(x)}\) is recognized as the definition of \(\tan(x)\). Therefore, the left hand side of the given identity is equal to the right hand side.

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