Is there a picture?
So we can figure it out
(tan²(<em>θ</em>) cos²(<em>θ</em>) - 1) / (1 + cos(2<em>θ</em>))
Recall that
tan(<em>θ</em>) = sin(<em>θ</em>) / cos(<em>θ</em>)
so cos²(<em>θ</em>) cancels with the cos²(<em>θ</em>) in the tan²(<em>θ</em>) term:
(sin²(<em>θ</em>) - 1) / (1 + cos(2<em>θ</em>))
Recall the double angle identity for cosine,
cos(2<em>θ</em>) = 2 cos²(<em>θ</em>) - 1
so the 1 in the denominator also vanishes:
(sin²(<em>θ</em>) - 1) / (2 cos²(<em>θ</em>))
Recall the Pythagorean identity,
cos²(<em>θ</em>) + sin²(<em>θ</em>) = 1
which means
sin²(<em>θ</em>) - 1 = -cos²(<em>θ</em>):
-cos²(<em>θ</em>) / (2 cos²(<em>θ</em>))
Cancel the cos²(<em>θ</em>) terms to end up with
(tan²(<em>θ</em>) cos²(<em>θ</em>) - 1) / (1 + cos(2<em>θ</em>)) = -1/2
Answer:
x = 8
I dunno what the question is in the first place, but I assume you are solving for x.
Step-by-step explanation:
The two given angles are equivalent because they are parallel and they have a line that intersects.
The line creates two angles on each side of each line, which is 120 or 60 because there are 180 degs on a straight line.
The obtuse side is 120, and the -8 + 16x is also on an obtuse angle, showing that they are equal.
120 = -8 + 16x
128 = 16x
8 = x
x = 8
Some information is missing for #6.
#7: use sine, sin35=h/5.1, h=5.1*sin35, use a calculator, h≈2.9
#23: to find the reference angle, keep subtracting the number by 360, until the remaining difference is the smallest positive number.
1406-360-360-360=326. the reference angle is 326.
now look at the remainder, the terminal line of 326 degree is in the 4th quadrant between 270 and 360, the the reference angle is 360-326=34, the angle between the terminal line and the positive x axis. 34 is the answer.
