Simplify (1+cos(x/2)-sin(x/2))/(1-cos(x/2)-s in(x/2))

Recall the double angle identities:

cos(x/2) = cos(x/4 + x/4) = cos²(x/4) - sin²(x/4)

sin(x/2) = sin(x/4 + x/4) = 2 sin(x/4) cos(x/4)

So

(1 + cos(x/2) - sin(x/2)) / (1 - cos(x/2) - sin(x/2))

= (1 + cos²(x/4) - sin²(x/4) - 2 sin(x/4) cos(x/4)) / (1 - cos²(x/4) + sin²(x/4) - 2 sin(x/4) cos(x/4))

sin²(x) + cos²(x) = 1, so

(1 + cos(x/2) - sin(x/2)) / (1 - cos(x/2) - sin(x/2))

= (2 cos²(x/4) - 2 sin(x/4) cos(x/4)) / (2 sin²(x/4) - 2 sin(x/4) cos(x/4))

= (cos(x/4) / sin(x/4)) • (2 cos(x/4) - 2 sin(x/4)) / (2 sin(x/4) - 2 cos(x/4))

=  (cos(x/4) / sin(x/4)) • (-1)

= - cot(x/4)

1. 3

2. 4

3. 1

hope this ! have a great day.

-wfz

the data of the detroit pistons in numerical order from least to greatest is 0.30, 0.37, 0.55, 0.62, 0.69, 0.72, 0.73, 0.75, 0.77, 0.78, 0.80, 0.81, 0.81, 0.83, 0.84, 0.89

the data of the miami heat in numerical order from least to greatest is 0.50, 0.50, 0.56, 0.57, 0.67, 0.72, 0.72, 0.72, 0.75, 0.75, 0.76, 0.81, 0.82, 0.90, 1.00, 1.00

the detroit pistons median : 1.52

the miami heat median: 1.47

the iqr of this data is 0.05