Answer:
<em>Answer: choice D.</em>
Step-by-step explanation:
<u>Trigonometric Functions</u>
We need to recall some properties and definitions of the trigonometric functions.


We need to simplify the following expression:

Substituting the identity for the secant:

Operating:

Substituting the definition of the tangent:

Correct choice D.
Answer:
7- (y/4)
Step-by-step explanation:
Answer:
<em>1+√3</em>
Step-by-step explanation:
Area of the triangle = 1/2 * base * height
Area of the triangle = 1/2 * AC * BD
We need to get AC
AC = AD+DC
Get base AD using SOH CAH TOA
tan 45 = 4/AD
AD = 4/tan45
AD = 4/1
AD = 4
Get DC
tan 30 = 4/DC
DC = 4/tan 30
DC = 4/(1/√3)
DC = 4√3
AC = 4 + 4√3
AC = 4(1+√3)
Get the Area of the triangle
<em>Area = 1/2 * 4 * 4(1+√3)</em>
<em>Area of the triangle = 1+√3</em>
The measures of the angles don't change when you translate a figure, because the entire figure is moving as a whole. Imagine having a paper parallelogram, moving it around and flipping it over. Not even dilations would change these angles (for reasons that can be pretty easily visualed but not really proven until geometry)