Chapter 7: Q. 82 (page 486)

Find the exact value of each expression.
$\tan (\frac{π}{4} - \cos^{- 1} \frac{3}{5})$

Short Answer

Expert verified

The value of the expression is $- \frac{1}{7}$

Step by step solution

Step 1. Given information

The given expression is $\tan (\frac{π}{4} - \cos^{- 1} \frac{3}{5})$

Step 2. Solve the expression

Let $α = \frac{π}{4}$ and $β = \cos^{- 1} \frac{3}{5}$

So,

$\tan α = 1 \tan β = \frac{4}{3}$

Now,

$\tan (α - β) = \frac{\tan α - \tan β}{1 + \tan α \cdot \tan β} = \frac{1 - \frac{4}{3}}{1 + 1 \cdot \frac{4}{3}} = \frac{- \frac{1}{3}}{\frac{7}{3}} = - \frac{1}{7}$

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Find the exact value of each expression.
$\tan (\frac{π}{4} - \cos^{- 1} \frac{3}{5})$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve the expression

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Find the exact value of each expression.
$\tan (\frac{π}{4} - \cos^{- 1} \frac{3}{5})$