Chapter 7: Q. 81 (page 486)

Find the exact value of each expression.
$\tan (\sin^{- 1} \frac{3}{5} + \frac{π}{6})$

Short Answer

Expert verified

The value of the expression is $\frac{48 + 25 \sqrt{3}}{39}$

Step by step solution

Step 1. Given information

The given expression is $\tan (\sin^{- 1} \frac{3}{5} + \frac{π}{6})$

Step 2. Solve the expression

Let $α = \sin^{- 1} \frac{3}{5}$ and $β = \frac{π}{6}$

So,

$\tan α = \frac{3}{4} \tan β = \frac{1}{\sqrt{3}}$

Now,

localid="1646561606613" $\tan (α + β) = \frac{\tan α + \tan β}{1 - \tan α \cdot \tan β} = \frac{\frac{3}{4} + \frac{1}{\sqrt{3}}}{1 - \frac{3}{4} \cdot \frac{1}{\sqrt{3}}} = \frac{3 \sqrt{3} + 4}{4 \sqrt{3} - 3} = \frac{3 \sqrt{3} + 4}{4 \sqrt{3} - 3} \times \frac{4 \sqrt{3} + 3}{4 \sqrt{3} + 3} = \frac{48 + 25 \sqrt{3}}{39}$

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Find the exact value of each expression.
$\tan (\sin^{- 1} \frac{3}{5} + \frac{π}{6})$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve the expression

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Short Answer

Step by step solution

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Find the exact value of each expression.
$\tan (\sin^{- 1} \frac{3}{5} + \frac{π}{6})$