Chapter 7: Q 60. (page 458)

In Problem, write each trigonometric expression as an algebraic expression in $u$ .
$\tan (\cos^{- 1} u)$

Short Answer

Expert verified

Trigonometric expression $\tan (c o s^{- 1} u)$ as an algebraic expression in $u$ is given by $\begin{array}{rcl} \frac{\sqrt{1 - u^{2}}}{u} \end{array}$ .

Step by step solution

Step 1. Given information

An expression is $\tan (\cos^{- 1} u)$ .

Step 2. Value of the expression in terms of u

Consider the expression $\tan (\cos^{- 1} u)$ .

Let $\cos^{- 1} u = x$

So, $u = \cos x$

Consider the following figure:

Side opposite to angle $x = \sqrt{1 - u^{2}}$

localid="1646562158872" $\begin{array}{rcl} \tan x & = & \frac{\sqrt{1 - u^{2}}}{u} \\ x & = & \tan^{- 1} (\frac{\sqrt{1 - u^{2}}}{u}) \end{array}$

Therefore,

$\begin{array}{rcl} \tan (\cos^{- 1} u) & = & \tan [\tan^{- 1} (\frac{\sqrt{1 - u^{2}}}{u})] \\ = & \frac{\sqrt{1 - u^{2}}}{u} \end{array}$

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In Problem, write each trigonometric expression as an algebraic expression in $u$ .
$\tan (\cos^{- 1} u)$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Value of the expression in terms of u

One App. One Place for Learning.

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In Problem, write each trigonometric expression as an algebraic expression in u.tancos-1u

Short Answer

Step by step solution

Step 1. Given information

Step 2. Value of the expression in terms of u

One App. One Place for Learning.

Most popular questions from this chapter

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In Problem, write each trigonometric expression as an algebraic expression in $u$ .
$\tan (\cos^{- 1} u)$