Which of the following are identities? Check all that apply.

Mathematics

2 answers:

Genrish500 [490]2 years ago

7 0

Answer:

B and C and D

Step-by-step explanation:

This will help,

Ivenika [448]2 years ago

7 0

Answer:

Options A and D.

Step-by-step explanation:

To check the identities we have to check each option given.

A. tan(x - π) = tanx

We take left hand side (L.H.S.) of the equation.

tan(π - x) = tanx [ since we know tan(π ± x) = tanx ]

So L.H.S. = R.H.S.

It's an identity.

B. sin(x + y) + sin(x - y) = 2cosx siny

We take L.H.S. first

sin(x + y) + sin(x - y)

= sinx coxy + siny cosx + sinx cosy - cosx siny

= 2sinx cosy ≠ R.H.S.

Option B is not an identity.

C. cos(x + y) - cos(x - y) = 2cosx cosy

We take L.H.S. of the equation.

cos(x + y) - cos(x - y) = cosx cosy - sinx siny - (cosx cosy + sinx siny)

= -2sinx siny ≠ R.H.S.

Therefore, option C is not an identity.

D. cos(x + y) + cos(x - y) = 2cosx cosy

We take L.H.S. of the equation.

cos(x + y) + cos(x - y) = cosx cosy - sinx siny + cosx cosy + sinx siny

= 2cosx cosy = R.H.S.

Therefore, option D is an identity.

Options A and D are the identities.

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For this case what we must do is use the law of cosines.
We then have the following equation:
$c ^ 2 = a ^ 2 + b ^ 2 - 2 * a * b * cos (x)
$
Where,
a, b: sides of the triangle
x: angle between sides a and b.
Substituting values we have:
$c^2 = 90^2 + 75^2 - 2*90*75*cos(85)
$
Clearing the value of c we have:
$c = \sqrt{ 90^2 + 75^2 - 2*90*75*cos(85)}$
Answer:
An expression that is equivalent to how many feet the oak trees are from each other is:
$c = \sqrt{ 90^2 + 75^2 - 2*90*75*cos(85)}$