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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)

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Halla el volumen de un prisma con base triangular donde la base tiene 4m y la altura de la base es de 6cm,asi como la altura del
Brut [27]

Answer:

triangular donde la base tiene 4m y la altura de la base es de 6cm,asi como la altura del prisma de 10m

6 0
3 years ago
The perimeter of a rectangle is 46 millimeters. The length of the rectangle can be represented by (3x+3), and its width can be r
Tamiku [17]

Answer:

The dimension of this rectangle = 2mm by 21mm

Where 2 mm = Width of the rectangle

21 mm = Length of the rectangle.

Step-by-step explanation:

The formula for the perimeter of a rectangle = 2(L + W)

= 2L + 2W

The perimeter = 46 mm

L = 3x + 3

W = x - 4

P = 2L + 2W

46mm = 2(3x + 3) + 2(x - 4)

46 = 6x + 6 + 2x - 8

Collect like terms

46 +8 -6 = 6x + 2x

48 = 8x

x = 48/8

x = 6

Since the Length = 3x + 3

= 3(6) + 3

= 18 + 3

= 21mm

Since the Width = x - 4

= 6 - 4

= 2mm

Therefore, the dimension of this rectangle = 2mm by 21mm

Where 2 mm = Width of the rectangle

21 mm = Length of the rectangle.

8 0
3 years ago
What is the equation of the line that passes through (-2, 2) and (1, -4)?
MrMuchimi

Answer:

y=−2x−2

Step-by-step explanation:

i hope it helps

have a good day ^_^

5 0
2 years ago
The quotient of 38 times a number and -4
nikdorinn [45]

Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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