Question

BRAINLIESTT ASAP! PLEASE HELP ME :)

Answer 1

Answer: D) none of the equations are identities

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Work Shown:

I'm going to use x in place of theta.

let

f(x) = sin(x+2pi/4)

g(x) = sqrt(2)*sin(x)*cos(x)

Plug in x = 0

f(x) = sin(x+2pi/4)

f(0) = sin(0+2pi/4)

f(0) = sin(2pi/4)

f(0) = sin(pi/2)

f(0) = 1

and

g(x) = sqrt(2)*sin(x)*cos(x)

g(0) = sqrt(2)*sin(0)*cos(0)

g(0) = sqrt(2)*0*1

g(0) = 0

We see that f(0) = g(0) is not a true equation

Therefore, f(x) = g(x) is not true for all values of x, making it not be an identity. We can use a graph to compare f(x) and g(x) to see that they do not line up.

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Let

h(x) = cos(x-pi/3)

i(x) = (3/sqrt(2))*(cos(x) - sin(x))

Plug in x = 0

h(x) = cos(x-pi/3)

h(0) = cos(0-pi/3)

h(0) = 0.5

and

i(x) = (3/sqrt(2))*(cos(x) - sin(x))

i(0) = (3/sqrt(2))*(cos(0) - sin(0))

i(0) = 2.12

Like with equation 1, we do not have an identity since h(0) does not equal i(0). We only need one counter example since an identity states that h(x) = i(x) for all values of x in the domain.

Answer 2

Answer:

2

Step-by-step explanation: