Chapter 7: Q. 20 (page 505)

use sum, difference, product, or half-angle formulas to find the exact value of each expression
$\tan (2 \sin^{- 1} (\frac{6}{11}))$

Short Answer

Expert verified

$\tan (2 \sin^{- 1} (\frac{6}{11})) = \frac{12 \sqrt{85}}{49}$

Step by step solution

Step 1.Given expression

$\tan (2 \sin^{- 1} (\frac{6}{11}))$

Step 2. Solving

let :

$\sin^{- 1} \frac{6}{11} = θ$

we need to find

$\tan 2 θ$

$\sin^{- 1} \frac{6}{11} = θ \sin θ = \frac{6}{11}$

Step 3. Solving for tan 2θ

$\tan 2 θ = \frac{\sin 2 θ}{\cos 2 θ} \tan 2 θ = \frac{2 \sin θ \cos θ}{1 - 2 \sin^{2} θ} \tan 2 θ = \frac{2 \sin θ \sqrt{1 - \sin^{2} θ}}{1 - 2 \sin^{2} θ} \tan 2 θ = \frac{2 \times \frac{6}{11} \sqrt{1 - {(\frac{6}{11})}^{2}}}{1 - 2 \times {(\frac{6}{11})}^{2}} \tan 2 θ = \frac{2 \times \frac{6}{11} \frac{\sqrt{85}}{11}}{\frac{49}{121}} \tan 2 θ = \frac{12 \sqrt{85}}{49}$

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use sum, difference, product, or half-angle formulas to find the exact value of each expression
$\tan (2 \sin^{- 1} (\frac{6}{11}))$

Short Answer

Step by step solution

Step 1.Given expression

Step 2. Solving

Step 3. Solving for tan 2θ

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use sum, difference, product, or half-angle formulas to find the exact value of each expressiontan(2sin-1(611))

Short Answer

Step by step solution

Step 1.Given expression

Step 2. Solving

Step 3. Solving for tan 2θ

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Decision Maths

Logic and Functions

Discrete Mathematics

Calculus

Geometry

Study anywhere. Anytime. Across all devices.

use sum, difference, product, or half-angle formulas to find the exact value of each expression
$\tan (2 \sin^{- 1} (\frac{6}{11}))$