<span> I am assuming you want to prove:
csc(x)/[1 - cos(x)] = [1 + cos(x)]/sin^3(x).
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<span>If we multiply the LHS by [1 + cos(x)]/[1 + cos(x)], we get:
LHS = csc(x)/[1 - cos(x)]
= {csc(x)[1 + cos(x)]/{[1 + cos(x)][1 - cos(x)]}
= {csc(x)[1 + cos(x)]}/[1 - cos^2(x)], via difference of squares
= {csc(x)[1 + cos(x)]}/sin^2(x), since sin^2(x) = 1 - cos^2(x).
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<span>Then, since csc(x) = 1/sin(x):
LHS = {csc(x)[1 + cos(x)]}/sin^2(x)
= {[1 + cos(x)]/sin(x)}/sin^2(x)
= [1 + cos(x)]/sin^3(x)
= RHS.
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<span>I hope this helps! </span>
3/4 foot is 9 inches, and 4 1/2 feet is 54 inches, so, 54/9 makes exactly 6 pieces of string.
A)
Two sides are 8 x 2 = 16 x 2 = 32 sq. in.
Two sides are 11 x 2 = 22 x 2 = 44 sq. in.
Top is 8 x 11 = 88 sq. in.
Total surface area: 32 + 44 + 88 = 164 square inches.
B) Area of a circle = PI x r^2
Area = 63.585
63.585 = PI x r^2
Using 3.14 for PI:
63.585 = 3.14 x r^2
Divide both sides by 3.14:
r^2 = 63.585 / 3.14
r^2 = 20.25
r = √20.25
radius = 4.5 inches.
C)
Diameter = radius x 2
Diameter = 4.5 x 2 = 9 inches.
Answer:
10%
Step-by-step explanation:
