Chapter 7: Q. 10 (page 485)

True or FalseIf $f (x) = \sin x$ and $g (x) = \cos x$ then $g (α + β) = g (α) g (β) - f (α) f (β)$ .

Short Answer

Expert verified

If $f (x) = \sin x$ and $g (x) = \cos x$ then localid="1646462766502" $g (α + β) = g (α) g (β) - f (α) f (β)$ .

This is true.

Step by step solution

Step 1. Given information

Given that:

$f (x) = \sin x g (x) = \cos x then g (α + β) = g (α) g (β) - f (α) f (β) .$

We have to tell whether this is true or false.

Step 2. Apply the sum of the cosine function

Consider the LHS.

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

Consider RHS.

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

Therefore, L.H.S.=R.H.S.

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True or FalseIf $f (x) = \sin x$ and $g (x) = \cos x$ then $g (α + β) = g (α) g (β) - f (α) f (β)$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. Apply the sum of the cosine function

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True or FalseIff(x)=sinx andg(x)=cosx then g(α+β)=g(α)g(β)-f(α)f(β).

Short Answer

Step by step solution

Step 1. Given information

Step 2. Apply the sum of the cosine function

One App. One Place for Learning.

Most popular questions from this chapter

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True or FalseIf $f (x) = \sin x$ and $g (x) = \cos x$ then $g (α + β) = g (α) g (β) - f (α) f (β)$ .