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Chapter 7: Q. 96 (page 475)

Establish each identity.
$\ln | \tan θ | = \ln | \sin θ | - \ln | \cos θ |$

Short Answer

Expert verified

The left side of the given equation has been simplified to bring the right side.

Step by step solution

01

Step 1. Given Information

The given equation is $\ln | \tan θ | = \ln | \sin θ | - \ln | \cos θ |$

02

Step 2. Calculation

Consider the left side of the given equation and simplify to bring the right side in order to establish the equation.
$\ln | \tan θ | = \ln | \frac{\sin θ}{\cos θ} | = \ln | \sin θ | - \ln | \cos θ |$

Hence, Proved

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Most popular questions from this chapter

If $x = 2 \tan θ$ , express $\sin (2 θ)$ as a function ofx.

Rewrite over a common denominator:

$\frac{\sin (θ) + \cos (θ)}{\cos (θ)} + \frac{\sin (θ) + \cos (θ)}{\sin (θ)}$

Express the product $\sin (4 θ) \sin (2 θ)$ as a sum containing only sines or only cosines.

If $z = \tan \frac{α}{2}$ , show that localid="1646416257885" $\cos α = \frac{1 - z^{2}}{1 + z^{2}}$ .

solve each equation on the interval

$0 \leq θ < 2 π$

$\sin θ + \cos θ = \sqrt{2}$

See all solutions

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