Prove the identity: (5 csc^2 x+4 csc x-1 / cot ^2 x) = (5 csc x-1 / csc x-1)?

Question

1. Prove the identity: (5 csc^2 x+4 csc x-1 / cot ^2 x) = (5 csc x-1 / csc x-1)

2. Prove the identity: csc^4 x - cot^4 x = csc^2 x + cot^2 x

3. The position of a weight attached to a spring is s(t) = -9 cos 8pit inches after t seconds. What is the maximum height that the weight reaches above the equilibrium position and when does it first reach the maximum weight.....
a) the max height of 18 inches is first reached after 2 seconds
b) the max height of 9 inches is first reached after 0.13 seconds
c) the max height of 9 inches is first reached after 4 seconds
d) the max height of 18 inches is first reached after 4 seconds


best answer gets 10 points!! please help me.

bonobo · Accepted Answer

Please use parentheses and brackets everywhere there is an ambiguity.

   (5csc^2[x] + 4) • (csc[x] − 1) ... and so on

 or  (5csc^2[x + 4]) • (csc[x − 1]) In this case only is the 4 and 1 in radians?

 or  ( 5csc^2[x] + 4csc[x] − 1 ) ...

 or  ...

Anonymous · Answer

a million. LHS= cos/sincos + (a million-cos^2x) +cos^2x 2. a million/sin +a million-cos^2x+cos^2x 3. a million/sin + a million 4. cosecx + a million =RHS you're welcome. observe: Use the RHS/LHS information approach with the intention to mathematically coach this identity.

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Prove the identity: (5 csc^2 x+4 csc x-1 / cot ^2 x) = (5 csc x-1 / csc x-1)?

2 Answers