In Exercises 1–60, verify each identity. tan x csc x cos x = 1

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Start by recalling the definitions of the trigonometric functions involved: $ \tan x = \frac{\sin x}{\cos x} $, $ \csc x = \frac{1}{\sin x} $, and $ \cos x = \cos x $.

Substitute these definitions into the left-hand side of the identity: $ \tan x \cdot \csc x \cdot \cos x = \left( \frac{\sin x}{\cos x} \right) \cdot \left( \frac{1}{\sin x} \right) \cdot \cos x $.

Simplify the expression by canceling out $ \sin x $ in the numerator and denominator: $ \frac{\sin x}{\cos x} \cdot \frac{1}{\sin x} = \frac{1}{\cos x} $.

Now, multiply the remaining terms: $ \frac{1}{\cos x} \cdot \cos x $.

Observe that $ \frac{1}{\cos x} \cdot \cos x = 1 $, thus verifying the identity.

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