1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
LekaFEV [45]
3 years ago
12

Please help me!!!!!​

Mathematics
1 answer:
Bas_tet [7]3 years ago
4 0

Answer:  see proof below

<u>Step-by-step explanation:</u>

Use the Sum & Difference Identity: tan (A - B) = (tanA - tanB)/(1 + tanA tanB)

Use the Half-Angle Identity: tan (A/2) = (1 - cosA)/(sinA)

Use the Unit Circle to evaluate tan (π/4) = 1

Use Pythagorean Identity:     cos²A + sin²A = 1

<u>Proof LHS → RHS</u>

\text{Given:}\qquad \qquad \qquad\dfrac{2\tan\bigg(\dfrac{\pi}{4}-\dfrac{A}{2}\bigg)}{1+\tan^2\bigg(\dfrac{\pi}{4}-\dfrac{A}{2}\bigg)}

\text{Difference Identity:}\qquad \dfrac{2 \bigg( \frac{\tan\frac{\pi}{4}-\tan\frac{A}{2}}{1+\tan\frac{\pi}{4}\cdot \tan\frac{A}{2}}\bigg)}{1+ \bigg( \frac{\tan\frac{\pi}{4}-\tan\frac{A}{2}}{1+\tan\frac{\pi}{4}\cdot \tan\frac{A}{2}}\bigg)^2}

\text{Substitute:}\qquad \qquad \dfrac{2 \bigg( \frac{1-\tan\frac{A}{2}}{1+\tan\frac{A}{2}}\bigg)}{1+ \bigg( \frac{1-\tan\frac{A}{2}}{1+\tan\frac{A}{2}}\bigg)^2}

\text{Simplify:}\qquad \qquad \qquad \dfrac{1-\tan^2\frac{A}{2}}{1+\tan^2\frac{A}{2}}

\text{Half-Angle Identity:}\qquad \quad \dfrac{1-(\frac{1-\cos A}{\sin A})^2}{1+(\frac{1-\cos A}{\sin A})^2}

\text{Simplify:}\qquad \qquad \dfrac{\sin^2 A-1+2\cos A-\cos^2 A}{\sin^2 A+1-2\cos A+\cos^2 A}

\text{Pythagorean Identity:}\qquad \qquad \dfrac{1-\cos^2 A-1+2\cos A}{2-2\cos A}

\text{Simplify:}\qquad \qquad \qquad \dfrac{2\cos A-2\cos^2 A}{2(1-\cos A)}\\\\.\qquad \qquad \qquad \qquad =\dfrac{2\cos A(1-\cos A)}{2(1-\cos A)}

                               =  cos A

LHS = RHS:  cos A = cos A   \checkmark

You might be interested in
Write each decimal as a precent 0.17
Tatiana [17]

Answer:

17%

Step-by-step explanation:

it's basically just 17/100 which would be 17%

3 0
3 years ago
Read 2 more answers
What does the slope of the line represent within the context of my graph
Nata [24]
The slope of the line is the velocity, or rate of change, of y with respect to x.  In other terms, the slope tells you how much y will change for every change in x by one unit.  For example if the slope, which is velocity, is 2.  y will increase by two units every time x increases by one unit.  Your graph is not pictured nor explained, so I cannot give you the specific context beyond the principle that the slope of a line is a constant velocity or rate of change.
7 0
3 years ago
Read 2 more answers
A= B + 3(4 - C) <br> B=5<br> C= 2<br> A=?
Trava [24]

Answer:

A = 11 i believe

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
3. A rectangular prism has dimensions of , 2, and in.
Anna007 [38]
It is 28 cubes i think hope i’m right
4 0
2 years ago
Read 2 more answers
7 lb in 12 oz equals blank ounces​
kenny6666 [7]

7lb in 12 oz equals blank ounces = 124 ounces

4 0
3 years ago
Other questions:
  • Convert the polar equation to rectangular coordinates. (Use variables x and y as needed.)
    6·1 answer
  • sales at flower shop were $814 this week. this is $131 less than the sales last week. what were last weeks sales?​
    9·1 answer
  • Given an arithmetic sequence with a3=5 and a5=19, find the 24th term.
    15·1 answer
  • Jacob and Sarah are saving money to go on a trip. They need at least $1975 in order to go. Jacob mows lawns and Sarah walks dogs
    10·1 answer
  • Solve please I don’t know how to do this.
    5·2 answers
  • Graph the equation y= x^2 - 2x - 8 on the accompanying set of axes. You must plot 5 points including the roots and the vertex.
    6·1 answer
  • What are the rate of change and the initial value of the function represented by the graph?
    6·1 answer
  • Plz help me NOW and I will mark you brainliest
    11·1 answer
  • Simply <br><br> 28 divided by 2 plus 3(8) minus (12-8)
    11·2 answers
  • Compare and contrast the following two equations. Determine if they are linear equations and explain why or why not.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!