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
ale4655 [162]
3 years ago
10

Prove: cos(x+y)/cosxsiny=coty-tanx

Mathematics
2 answers:
Doss [256]3 years ago
8 0
Cos (x+y)/cos x sin y    

= cos x cos y - sin x sin y  / cos x sin y

= cos x cos y/cos x sin y     - sin x sin y / cos x sin y

hope this helps
Agata [3.3K]3 years ago
5 0

Answer:

Use Cosine Sum identity

Step-by-step explanation:

It's a simple demonstration if you know what trigonometric identity you should use. In this case use cosine sum identity which states:

cos(a+b)=cos(a)*cos(b)-sin(a)*sin(b)

Also keep in mind this property of fractions:

\frac{a \pm b}{c} =\frac{a}{c} \pm \frac{b}{c} \hspace{3} c\neq0

Using the previous information:

\frac{cos(x+y)}{cos(x)*sin(y)}=\frac{cos(x)*cos(y)-sin(x)*sin(y)}{cos(x)*sin(y)}=\frac{cos(x)*cos(y)}{cos(x)*sin(y)}-\frac{sin(x)sin(y)}{cos(x)*sin(y)}\\    \\=\frac{cos(y)}{sin(y)} -\frac{sin(x)}{cos(x)}

Also, according to the basic identities:

\frac{cos(\theta)}{sin(\theta)} =cot(\theta)\\\\\frac{sin(\theta)}{cos(\theta)}= tan(\theta)

Therefore:

\frac{cos(x+y)}{cos(x)*sin(y)}=\frac{cos(y)}{sin(y)} -\frac{sin(x)}{cos(x)}=cot(y)-tan(x)

You might be interested in
Calculate the area of this trapezium.<br> 7.9 cm<br> 6.2 cm<br> 10.8 cm
cestrela7 [59]

Answer:

A = 57.97 cm²

Step-by-step explanation:

The area (A) of a trapezium is calculated as

A = \frac{1}{2} h (a + b)

where h is the perpendicular height and a, b the parallel bases

Here h = 6.2, a = 10.8 and b = 7.9, thus

A = \frac{1}{2} × 6.2 × (10.8 + 7.9) = 3.1 × 18.7 = 57.97 cm²

5 0
3 years ago
What is the area: triangle with base of 14 in and height 10 in
Anika [276]
Triangle area formula: base*height/2
so, 14*10/2 = 7*10 = 70 sq. in.
7 0
3 years ago
Read 2 more answers
Lucia earns $150 each week. She saves 12% of her earnings.
tatiyna
$18 i think............
5 0
2 years ago
Read 2 more answers
10 points <br><br> slope of (-2,-4) and (6,7)<br> (explain)
Finger [1]

Answer:

11/-8

Step-by-step explanation:

-2-6=-8

-4-7=11

then flip

4 0
2 years ago
(15-3)÷12+1<br>How to divide this without using a remainder?​
Julli [10]

Answer:

If you solved this, it wouldn't have a remainder. First you would solve the numbers in the parenthesis, (15 - 3), which is 12. Now it should look like, 12 ÷ 12 + 1. Next you divide 12 by 12 and that equals 1. And all you need to do now is add 1 + 1, which is 2. So your answer will be 2.

8 0
3 years ago
Read 2 more answers
Other questions:
  • Brian has 3 basketball cards and 5 baseball cards.  What fraction of Brian's cards are baseball cards?
    10·2 answers
  • Write inequalities to describe the solid left (x &lt; 0 is left) hemisphere of a sphere of radius 4 centered at the origin
    14·2 answers
  • Giving 50 points if you can answer this. PLEASE HELP ME ATTACHMENT BELOW
    10·2 answers
  • I need help can someone pls find the answer
    15·1 answer
  • Given: JK tangent, KH=16, HE=12 Find: JK.
    6·1 answer
  • 5% of what number is 300?
    9·2 answers
  • A positive integer is twice another.the sum of the reciprocal of the two positive integer is 3/14. Find the integers
    6·1 answer
  • The local museum had 10,000 visitors in 1995.
    14·1 answer
  • Suppose a team is to be formed consisting of a head chef, sous chef, and dishwasher, in that order. What is the probability of f
    15·1 answer
  • What is the equation of the following line? Be sure to scroll down first to see
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!