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Tasya [4]
3 years ago
13

A function is created to represent the amount of money you save or spend each day of the week. What restrictions would be made t

o the range?
A) The range would only include integers.
B) The range would only include positive integers.
C) The range would only include negative integers.
D) The range would include all real numbers.
Mathematics
1 answer:
ollegr [7]3 years ago
6 0

The range would only include positive integers.

Answer B

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Help please!
KengaRu [80]

Answer:  see proof below

<u>Step-by-step explanation:</u>

Use the following Sum to Product Identities:

\cos A+\cos B=2\cos \bigg(\dfrac{A+B}{2}\bigg)\cdot \cos \bigg(\dfrac{A-B}{2}\bigg)\\\\\\\sin A-\sin B=2\cos \bigg(\dfrac{A+B}{2}\bigg)\cdot \sin \bigg(\dfrac{A-B}{2}\bigg)

Use Even/Odd Identities:    cos (-A) = - cos A

                                             sin (-A) =   sin (A)

Use Quotient Identity:   \cot A=\dfrac{\cos A}{\sin A}

<u>Proof LHS →  RHS:</u>

\text{LHS:}\qquad \qquad \qquad \dfrac{\cos x+\cos 7x}{\sin x - \sin 7x}

\text{Sum to Product:}\qquad \dfrac{2\cos \bigg(\dfrac{x+7x}{2}\bigg)\cdot \cos \bigg(\dfrac{x-7x}{2}\bigg)}{2\cos \bigg(\dfrac{x+7x}{2}\bigg)\cdot \sin \bigg(\dfrac{x-7x}{2}\bigg)}

\text{Simplify:}\qquad \qquad \quad \dfrac{2\cos \bigg(\dfrac{8x}{2}\bigg)\cdot \cos \bigg(\dfrac{-6x}{2}\bigg)}{2\cos \bigg(\dfrac{8x}{2}\bigg)\cdot \sin \bigg(\dfrac{-6x}{2}\bigg)}

                          = \dfrac{ \cos (-3x)}{\sin(-3x)}

\text{Even Odd:}\qquad \quad  \dfrac{ -\cos (3x)}{\sin(3x)}

\text{Quotient:}\qquad \quad -\cot(3x)

LHS = RHS  \checkmark

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