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lutik1710 [3]
3 years ago
11

Prove the identity. tan(x − y) + tan(z − x) + tan(y − z) = tan(x − y) tan(z − x) tan(y − z)

Mathematics
1 answer:
Viktor [21]3 years ago
4 0

Step-by-step explanation:

This is known as the triple tangent identity.  Start with the fact that the three angles add up to 0.

(x − y) + (z − x) + (y − z) = 0

Subtract two terms to the other side and take the tangent:

x − y = -((z − x) + (y − z))

tan(x − y) = tan(-((z − x) + (y − z)))

Use reflection property:

tan(x − y) = -tan((z − x) + (y − z))

Now use angle sum identity:

tan(x − y) = -[tan(z − x) + tan(y − z)] / [1 − tan(z − x) tan(y − z)]

tan(x − y) = [tan(z − x) + tan(y − z)] / [tan(z − x) tan(y − z) − 1]

tan(x − y) [tan(z − x) tan(y − z) − 1] = tan(z − x) + tan(y − z)

tan(x − y) tan(z − x) tan(y − z) − tan(x − y) = tan(z − x) + tan(y − z)

tan(x − y) tan(z − x) tan(y − z) = tan(x − y) + tan(z − x) + tan(y − z)

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Lunna [17]
To solve this problem we first call x = number of action figures, y = number of dolles. A system of two equations with two unknowns must be made to describe the problem. The system is the following:
 (x + 1) + y = 13
 1/2 * x = y.
 Then solving the system we have that x = 8 and y = 4.
 Since we know that the number of action figures is twice as many dolls plus one, then x = 8 + 1 = 9.
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3 0
3 years ago
Show in form of p by q 0.235​
VLD [36.1K]

Answer:

p = 235, q = 1000

Step-by-step explanation:

\frac{p}{q}  =  \frac{235}{1000}  \\

5 0
3 years ago
Which statement is always true? A. Square BCDF is a rectangle. B. Rectangle GJKM is a square. C. Quadrilateral STPR is a trapezo
Ivahew [28]

Answer:

Correct option is A

Step-by-step explanation:

Given some statements we have to choose the correct statement.

A. Square BCDF is a rectangle.

As we know, all the properties of rectangle satisfied by square. Therefore, we say that all squares are rectangles. hence, Square BCDF is a rectangle is true statement.

B. Rectangle GJKM is a square.

As explained in above, all the properties of rectangle satisfied by square but its converse is not true i.e all rectangles are not square. Hence, Rectangle GJKM is a square is not always true.

C. Quadrilateral STPR is a trapezoid.

All the properties of trapezoid are not satisfied by all quadrilateral hence, not always true.

D. Parallelogram ABCD is a rhombus

All the properties of rhombus are not satisfied by parallelogram like all sides of rhombus are congruent but parallelogram has only opposite sides congruent. hence, not always true.

Correct option is A.

8 0
3 years ago
Consider the first three terms of the sequence below. 14,000, 12,600, 11,340...
Naddika [18.5K]

Answer:

I think f(1) = is 14,000

Step-by-step explanation:

f(1) = 14,000 should be right but thats about all I know. Sorry.

4 0
3 years ago
dan painted 3/4 of a wall using 1/4 of a can of paint. how many walls can he paint using one can of paint?
Olenka [21]
3/4         x
 ÷     =   ÷
1/4        1

(4)  1/4x = 3/4  (4)

1x=3

final answer: dan can paint 3 walls
5 0
3 years ago
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