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
Ainat [17]
2 years ago
6

If a cot α = 1 and b cos α = 1, find a2 – b 2​

Mathematics
1 answer:
S_A_V [24]2 years ago
4 0

The equivalent expression of the<u> different of two square</u> is -1

Given the following expressions

a cot α = 1

a = 1/cot α = sinα/cosα

b = 1/cos α

We are to find the expression a² - b²

According to <u>difference of two squares;</u>

a² - b² =  (a + b) (a - b)

Substitute the given expressions into the formula as shown:

a^2 - b^2 = (\frac{sin \alpha}{cos \alpha} )^2 - (\frac{1}{cos \alpha} )^2\\a^2 - b^2=\frac{sin^2 \alpha}{cos^2 \alpha} -\frac{1}{cos ^2 \alpha}\\a^2 - b^2=\frac{sin^2 \alpha-1}{cos^2\alpha}\\a^2 - b^2=\frac{-(1-sin^2\alpha)}{cos^2\alpha} \\a^2 - b^2=\frac{-os^2 \alpha}{cos^2 \alpha}\\a^2 - b^2 = -1

This shows that the equivalent expression of the<u> difference of two squares</u> is -1

Learn more here: brainly.com/question/11084694

You might be interested in
Express the complex number in trigonometric form. -6 + 6 square root of 3 i ?
bagirrra123 [75]
\bf \begin{array}{clclll}&#10;-6&+&6\sqrt{3}\ i\\&#10;\uparrow &&\uparrow \\&#10;a&&b&#10;\end{array}\qquad &#10;\begin{cases}&#10;r=\sqrt{a^2+b^2}\\&#10;\theta =tan^{-1}\left( \frac{b}{a} \right)&#10;\end{cases}\qquad r[cos(\theta )+i\ sin(\theta )]\\\\&#10;-------------------------------\\\\

\bf r=\sqrt{(-6)^2+(6\sqrt{3})^2}\implies r=\sqrt{36+(6^2\cdot 3)}\implies r=\sqrt{144}&#10;\\\\\\&#10;r=12\leftarrow &#10;\\\\\\&#10;\theta =tan^{-1}\left( \frac{6\sqrt{3}}{-6} \right)\implies \theta =tan^{-1}\left( -\sqrt{3}\right)\implies \theta =&#10;\begin{cases}&#10;\frac{2\pi }{3}\leftarrow \\&#10;\frac{5\pi }{3}&#10;\end{cases}

now, notice, there are two valid angles for such a tangent, however, if we look at the complex pair, the "a" is negative and the "b" is positive, that means, "x" is negative and "y" is positive, and that only occurs in the 2nd quadrant, so the angle is in the second quadrant, not on the fourth quadrant.

thus         \bf 12\left[cos\left( \frac{2\pi }{3} \right) +i\ sin\left( \frac{2\pi }{3} \right) \right]
5 0
3 years ago
Question 5 (1 point)
sdas [7]

Answer:

C

Step-by-step explanation:

Normal distribution has a unique characteristic of having equal mean and median values. If mean was higher than median, then the distribution would be positively skewed. Mean lower than median would appear in distributions negatively skewed. Each data set has a median value.

3 0
3 years ago
4 friends earn $10.40 for washing a car. how each did each friend get
uysha [10]

Answer:

$2.60

Step-by-step explanation:


6 0
3 years ago
Read 2 more answers
James wants to build a wooden planter box for his garden with a volume of 100 cubic feet. If he constructed the planter with a h
EastWind [94]

Answer:

The length of the box is 10 feet.

Step-by-step explanation:

You have to work backwards to find volume, so just divide the volume (100) by the height (2) then divide that by the width (5) and you get your answer, 10

7 0
3 years ago
If Ray earns $120 for 15 hours of work how much will he earn for 20 hours of work at the same rate​
Free_Kalibri [48]
Find his rate:
120 / 15 = $8 per hour
Multiply the rate by hours:
$8 x 20 hours = $160
He will earn $160
8 0
3 years ago
Other questions:
  • F(x)=1.01(2)x rate of change from x=12 to x=15
    9·1 answer
  • Ln(2m 8th power) exapnad in logarithmic expression
    9·1 answer
  • What is the probability that two events, A and B, will occur at the same time?
    11·1 answer
  • Ms Ramos's thumb measures 4 centimeters express the length in meters
    15·2 answers
  • QUICK QUESTION PLEASE. help.
    8·1 answer
  • Please help with this question
    12·1 answer
  • Calculate the total surface area of the triangular pyramid.
    13·1 answer
  • What is the equation of the line on the graph?<br> i need help plzz can anyone help me
    12·1 answer
  • Christian is training for a swimming competition He starts swimming 10 ft. from the shore to his boat The table below represents
    9·2 answers
  • Lol dingus mcpringus
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!