<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>
The derivative of f(x) at x=3 is 2x=6 approaching from the left side (apply power rule to y=x^2). The derivative of f(x) at x=3 is m approaching from the right side. In order for the function to be differentiable, the limit of derivative at x=3 must be the same approaching from both sides, so m=6. Then, x^2=mx+b at x=3, plug in m=6, 9=18+b, so b=-9.
Why An Emergency Fund<span> Is Important. People who've had large and unforeseen expenses arise can probably either tell you how happy they were that they had</span>emergency fund<span>s, or how difficult it was to find the money to cover expenses.</span>
All you have to do here is some simplifying.
6/12 = what
6 divided by 12 = 1/2
1/2 = 2/4
There! We have our missing value
6/12 = 2/4
Answer: c = 4
Answer: Sphere
Step-by-step explanation:
