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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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answer
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9514 1404 393

Answer:

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Step-by-step explanation:

A. The matrix A has a row for each equation and a column for each variable. The entries in each column of a given row are the coefficients of the corresponding variable in the equation the row represents. If the variable is missing, its coefficient is zero.

This system of equations has 3 equations in 3 variables, so matrix A has dimensions ...

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Matrix A is 3×3.

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The coefficients of the variables are 0, 1, 5. These are the entries in row 2 of matrix A.

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C. As stated in part A, the size of matrix A will match the number of equations and variables in the system. If the number of variables remains the same, the number of rows of A (and b) will reflect the number of equations. (The number of columns of A (and rows of x) will reflect the number of variables.)

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