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Chapter 7: Q. 5 (page 495)

True or False. $\sin (2 θ)$ has two equivalent forms:
$2 \sin u \cos u$ and $\sin^{2} θ - \cos^{2} θ$

Short Answer

Expert verified

The given statement is false.

Step by step solution

01

Step 1. Given information

Two equivalent forms of $\sin 2 θ$ are given i.e., $2 \cos θ \sin θ$ and $\sin^{2} θ - \cos^{2} θ$

02

Step 2. True or False

From double angle formula, we know that:

$\sin 2 θ = 2 \sin θ \cos θ$ but

$\sin 2 θ \neq \sin^{2} θ - \cos^{2} θ$

So, this statement is false.

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Most popular questions from this chapter

Establish each identity.

$\frac{1}{1 - \sin θ} + \frac{1}{1 + \sin θ} = 2 s e c^{2} θ$

find the exact value of the expression

sin 285 $°$ sin 75 $°$

solve each equation on the interval

$\sqrt{3} \sin θ + \cos θ = 1$

Establish each identity.

$\frac{\cos θ + \sin θ - \sin^{3} θ}{\sin θ} = c o t θ + \cos^{2} θ$

In Problems 9–36, find the exact value of each expression.

$\csc [\cos^{- 1} (- \frac{\sqrt{3}}{2})]$

See all solutions

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