Chapter 7: Q. 99 (page 475)

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

Short Answer

Expert verified

Yes, the functions are identically equal.

Step by step solution

Step 1. Given Information

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

Step 2. Calculation

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

$g (x) = s e c x - \cos x = \frac{1}{\cos x} - \cos x = \frac{1 - \cos^{2} x}{\cos x} = \frac{\sin^{2} x}{\cos x} = \sin x \tan x = f (x)$

Thus, both the functions are equal.

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

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

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Most popular questions from this chapter

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