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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Answer:
(a)
$850.
(b)
$4250.
(c)
$4267.
Step-by-step explanation:
It is given that the value of a new car decreases by about 15% in the first year.
(a)
Now we are asked to find the cost of a car after one year; if we are given the initial value of car=$1000.
As the rate decreases by 15%.
that means we have to pay (100-15)% of the initial amount.
i.e. we have to pay 85% of the initial amount.
Hence the amount one has to pay= 85% of 1000.
which is equal to =85%×1000
⇒ =
Hence, the amount of car after one year when initaial amount is $1000 is:
$850.
(b)
if initial amount=$ 5000
then amount one has to pay after one year:

Hence, the amount of car after one year when initaial amount is $5000 is:
$4250.
(c)
if initial amount=$ 5020
then amount one has to pay after one year:

Hence, the amount of car after one year when initaial amount is $5020 is:
$4267.
Answer:
Mean = 58.25
Median = 57.5
Mode = 49
Step-by-step explanation:
We are given the following data set:
55, 51, 74, 61, 67, 60, 49, 49
Formula:

Sorted data:
49, 49, 51, 55, 60, 61, 67, 74
Mode is the entry with highest frequency.
49 appeared two times.
Mode = 49
Formula:

All these are less than 60 seconds, which indicates that students perceive 1 minute to pass sooner than it actually has.