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Chapter 7: Q. 9 (page 485)

True or False $\cos (\frac{π}{2} - θ) = \cos θ$

Short Answer

Expert verified

$\cos (\frac{π}{2} - θ) = \cos θ$ is false.

Step by step solution

01

Step 1. Given information

Given that $\cos (\frac{π}{2} - θ) = \cos θ$ .

We have to tell whether this is true or false.

02

Step 2. Apply the difference of cosine function

We know $\cos (α - β) = \cos α \cos β + \sin α \sin β$ .

$\cos (\frac{π}{2} - θ) = \cos \frac{π}{2} \cos θ + \sin \frac{π}{2} \sin θ = 0 \cos θ + 1 \sin θ = \sin θ$

Therefore, $\cos (\frac{π}{2} - θ) = \cos θ$ is false.

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Most popular questions from this chapter

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

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

$\cos (α + β) = \cos α \cos β_______\sin α \sin β$

if $\sin α = - \frac{4}{5}$ , $π < α < \frac{3 π}{2}$ , then $\cos α =$ _____

$\tan^{2} (θ) - \sec^{2} (θ)$

Establish each identity.

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

See all solutions

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