By using the AAA congruence property of Triangles, △aec≅△deb is proved
It is given two triangles, Δaec and Δdeb, where e is the common point known as the midpoint of ad
Also, it is given that,
ca ║db
We need to prove that, △aec≅△deb
Then we'll use AAA congruence property of Triangles to prove the situation
As ca ║db
then, ∠cae = ∠ebd (Alternate angles)
∠ace = ∠edb (Alternate angles)
and ∠aec = ∠deb (common angles)
Thus, by AAA congruence property, △aec≅△deb
Hence, proved
To learn more about, congruence property, here
brainly.com/question/2039214
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(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
To determine the missing angle you simply subtract the angle you know from 180 because a flat line is 180 degrees. If it is a circle you subtract the number from 360. Hope this helps!