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Chapter 7: Q.2 (page 473)

True or False: $\sin (- θ) + \cos (- θ) = \cos (θ) - \sin (θ)$

Short Answer

Expert verified

The given identity is true

Step by step solution

01

Given information

We are given a identity $\sin (- θ) + \cos (- θ) = \cos (θ) - \sin (θ)$

02

Explanation for true statement

We know that,

$\sin (- θ) = - \sin (θ) \cos (- θ) = \cos (θ)$

On adding these two we get,

$\sin (- θ) + \cos (- θ) = \cos (θ) - \sin (θ)$

Hence the given statement is true statement

03

Conclusion

The given identity is true

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Most popular questions from this chapter

True or False: $\sin (- θ) + \sin (θ) = 0$ for any value of theta

Rewrite in terms of sine and cosine functions: $\tan (θ) c s c (θ)$

Establish each identity.

$\frac{1 - 2 \cos^{2} θ}{\sin θ \cos θ} = \tan θ - c o t θ$

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

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

$\sec [\sin^{- 1} (- \frac{1}{2})]$

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