Chapter 7: Q. 6 (page 485)

$\sin (α - β) = \sin α \cos β___\cos α \sin β$

Short Answer

Expert verified

$\sin (α - β) = \sin α \cos β - \cos α \sin β$

Step by step solution

Step 1. Given information

We have been given $\sin (α - β) = \sin α \cos β___\cos α \sin β$ .

We have to fill in the blank.

Step 2. Use the sum formula for the sine function

Sum of the sine function is $\sin (α + β) = \sin α \cos β + \cos α \sin β$ .

Substitute $β$ with $- β$ .

$\sin (α + (- β)) = \sin α \cos (- β) + \cos α \sin (- β) \sin (α - β) = \sin α \cos β - \cos α \sin β (\cos (- β) = cosβ and \sin (- β) = - sinβ)$

Therefore, $\sin (α - β) = \sin α \cos β - \cos α \sin β$

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$\sin (α - β) = \sin α \cos β___\cos α \sin β$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Use the sum formula for the sine function

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sin(α-β)=sinαcosβ___cosαsinβ

Short Answer

Step by step solution

Step 1. Given information

Step 2. Use the sum formula for the sine function

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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$\sin (α - β) = \sin α \cos β___\cos α \sin β$