cosθ = cotθ/cscθ is a true statement. The answer is option B
<h3>How to determine which of the trigonometric statements are true?</h3>
Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles
A. tan²θ = 1 - sec²θ
tan²θ = 1 - sec²θ
tan²θ = 1 - 1/cos²θ (Note: sec²θ = 1/cos²θ)
tan²θ = (cos²θ- 1)/cos²θ
tan²θ = -sin²θ/cos²θ (Note: cos²θ- 1 = -sin²θ)
tan²θ = -tan²θ
This statement is not true
B. cosθ = cotθ/cscθ
cosθ = cotθ/cscθ
cosθ = (1/tanθ) / (1/sinθ)
cosθ = (cosθ/sinθ).sinθ
cosθ = cosθ
This statement is true
C. 1/sec²θ = sin²θ + 1
1/sec²θ = 1/(1/cos²θ)
1/sec²θ = cos²θ
1/sec²θ = 1 - sin²θ
This statement is not true
D. sec²θ - 1 = 1/cot²θ
sec²θ - 1 = 1/cos²θ - 1
sec²θ - 1 = (1-cos²θ)/cos²θ
sec²θ - 1 = sin²θ/cos²θ
sec²θ - 1 = tan²θ
This statement is not true
E. sinθ cscθ = tan θ
sinθ cscθ = tan θ
sinθ cscθ = sinθ (1/sinθ)
sinθ cscθ = 1
This statement is not true
Therefore, the true statement is cosθ = cotθ/cscθ
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number one is the last one
second is the third
third is the last
Answer:
A. We have two lines: y = 2-x and y = 4x+3 Given two simultaneous equations that are both required to be true.. the solution is the points where the lines cross... Which is where the two equations are equal.. Thus the solution that works for both equations is when 2-x = 4x+3 because where that is true is where the two lines will cross and that is the common point that satisfies both equations. B. 2-x = 4x+3 x 2-x 4x+3
______________
-3 5 -9
-2 4 -5
-1 3 -1
0 2 3
1 1 7
2 0 11
3 -1 15
The table shows that none of the integers from [-3,3] work because in no case does
2-x = 4x+3 To find the solution we need to rearrange the equation to the form x=n 2-x = 4x+3 2 -x + x = 4x + x +3 2 = 5x + 3 2-3 = 5x +3-3 5x = -1 x = -1/5 The only point that satisfies both equations is where x = -1/5 Find y: y = 2-x = 2 - (-1/5) = 2 + 1/5 = 10/5 + 1/5 = 11/5 Verify we get the same in the other equation y = 4x + 3 = 4(-1/5) + 3 = -4/5 + 15/5 = 11/5 Thus the only actual solution, being the point where the lines cross, is the point (-1/5, 11/5) C. To solve graphically 2-x=4x+3 we would graph both lines... y = 2-x and y = 4x+3 The point on the graph where the lines cross is the solution to the system of equations ... [It should be, as shown above, the point (-1/5, 11/5)] To graph y = 2-x make a table.... We have already done this in part B x 2-x x 4x+3 _______ ________ -1 3 -1 -1 0 2 0 3 1 1 1 7 Just graph the points on a cartesian coordinate system and draw the two lines. The solution is, as stated, the point where the two lines cross on the graph.
Hope this helps.
Step-by-step explanation:
Answer:
add the equation to eliminate the variable
