Answer:
Step-by-step explanation:
Using the addition formulae for cosine
cos(x ± y) = cosxcosy ∓ sinxsiny
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cos(120 + x) = cos120cosx - sin120sinx
= - cos60cosx - sin60sinx
= - 
cosx - 
sinx
squaring to obtain cos² (120 + x)
= 
cos²x + sinxcosx + 
sin²x
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cos(120 - x) = cos120cosx + sin120sinx
= -cos60cosx + sin60sinx
= - cosx + sinx
squaring to obtain cos²(120 - x)
= cos²x - sinxcosx + sin²x
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Putting it all together
cos²x + cos²x + sinxcosx + sin²x + cos²x - sinxcosx + sin²x
= cos²x + cos²x + sin²x
= cos²x + sin²x
= (cos²x + sin²x) =
Answer:
x ∈ (-∞, -1) ∪ (1, ∞)
Step-by-step explanation:
To solve this problem we must factor the expression that is shown in the denominator of the inequality.
So, we have:
So the roots are:
Therefore we can write the expression in the following way:
Now the expression is as follows:
Now we use the study of signs to solve this inequality.
We have 3 roots for the polynomials that make up the expression:
We know that the first two are not allowed because they make the denominator zero.
Observe the attached image.
Note that:
when 
when 
and
is always 
Finally after the study of signs we can reach the conclusion that:
x ∈ (-∞, -1) ∪ (1, 2] ∪ [2, ∞)
This is the same as
x ∈ (-∞, -1) ∪ (1, ∞)
The area of the rectangle is 
units.
Step-by-step explanation:
Step 1:
The area of a rectangle is obtained by multiplying the length with the width of the rectangle.
Considering this a whole rectangle, the length of the rectangle is 5 units and the width is the sum of 
, 
, and -6.
So the length of the rectangle = 5 units and
the width of the rectangle 
units.
The area of a rectangle = (length)(width).
Step 2:
By substituting the known values, we get
The area of the rectangle 
So the area of the rectangle is units.
