Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identity
• 1 + cot²x = csc²x
Consider the left side
x -
x
Factorise as a difference of squares
= (csc²x - cot²x)(csc²x + cot²x)
= (1 + cot²x - cot²x)(csc²x + cot²x)
= csc²x + cot²x
= csc²x + csc²x - 1
= 2csc²x - 1 = right side ⇒ verified
Answer:
21
Step-by-step explanation:
Using<em> Simple Random Sampling</em>, we can estimate the sample size by the formula
where
n = sample size
Z = the z-score corresponding to the confidence level 99.5%
S = the assumed standard deviation = 3 seconds
e = margin of error = 2 seconds
<em>It is worth noticing that the higher the confidence level, the larger the sample should be. </em>
The z-score corresponding to a confidence level of 99.5% can be obtained either with a table or the computer and equals
Z = 3.023
Replacing the values in our formula
So the size of the sample should be at least 21.