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Chapter 5: Problem 35

Verify the identity. $$\frac{\tan x \cot x}{\cos x}=\sec x$$

Short Answer

Expert verified
The given identity \( \frac{\tan x \cot x}{\cos x} = \sec x \) is verified.

Step by step solution

01

Express all functions in terms of sine and cosine

Firstly, replace all trigonometric terms from the left side of the equation with their equivalent in terms of sine and cosine, to simplify the expression. Given \( \frac{\tan x \cot x}{\cos x} \), the reformation will result in \( \frac{(\frac{\sin x}{\cos x} )(\frac{\cos x}{\sin x})}{\cos x} \).
02

Simplify the expression

By cancelling the corresponding terms in numerator and denominator, the equation simplifies to \( \frac{1}{\cos x} \).
03

Final result

The final result \( \frac{1}{\cos x} \) equals to \( \sec x \), thus proving the given identity.

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