Chapter 7: Q. 100 (page 475)

Show that the functions f and g are identically equal.
$f (x) = \cos x \cdot c o t x, g (x) = c s c x - \sin x$

Short Answer

Expert verified

Yes, the functions are identically equal.

Step by step solution

Step 1. Given Information

The given functions are $f (x) = \cos x \cdot c o t x, g (x) = c s c x - \sin x$

Step 2. Calculation

Simplify any one function and determine whether they are equal or not to the other function.

$f (x) = \cos x \cdot c o t x = \cos x \frac{\cos x}{\sin x} = \frac{\cos^{2} x}{\sin x} = \frac{1 - \sin^{2} x}{\sin x} = \frac{1}{\sin x} - \sin x = c s c x - \sin x = g (x)$

Thus, both the functions are equal.

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Show that the functions f and g are identically equal.
$f (x) = \cos x \cdot c o t x, g (x) = c s c x - \sin x$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

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