1)
LHS = cot(a/2) - tan(a/2)
= (1 - tan^2(a/2))/tan(a/2)
= (2-sec^2(a/2))/tan(a/2)
= 2cot(a/2) - cosec(a/2)sec(a/2)
= 2(1+cos(a))/sin(a) - 1/(cos(a/2)sin(a/2))
= 2 (1+cos(a))/sin(a) - 2/sin(a)) (product to sums)
= 2[(1+cos(a) -1)/sin(a)]
=2cot a
= RHS
2.
LHS = cot(b/2) + tan(b/2)
= [1 + tan^2(b/2)]/tan(b/2)
= sec^2(b/2)/tan(b/2)
= 1/sin(b/2)cos(b/2)
using product to sums
= 2/sin(b)
= 2cosec(b)
= RHS
5 hours and 30 minutes or 5.5 hours
Answer:
<h3><u>Mean</u></h3>
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<h3><u>Standard Deviation</u></h3>



<h3><u>Summary</u></h3>
Nilo has a mean score of 10 and a standard deviation of 5.23.
Lisa has a mean score of 10 and a standard deviation of 1.83.
The <u>mean</u> scores are the <u>same</u>.
Nilo's standard deviation is higher than Lisa's. Therefore, Nilo's test scores are more <u>spread out</u> that Lisa's, which means Lisa's test scores are more <u>consistent</u>.
<u>Given</u>:
Given that an aquarium is being filled with water.
The given graph shows the height of the water over time as the aquarium is being filled.
We need to determine the slope of the graph.
<u>Slope</u>:
The slope of the given graph can be determined using the formula,

Since, the slope is same for all the points on the straight line, then let us consider the points (2,5) and (4,10)
Substituting these points in the above formula, we get;

Simplifying, we get;


Thus, the slope of the given graph is 2.5
The Number is 79500, since the nearest thousand for 79500 is 80000