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maksim [4K]
3 years ago
8

Csc2theta=csctheta/2costhetaCan you help verify the identity

Mathematics
1 answer:
Yakvenalex [24]3 years ago
7 0

csc(2x) = csc(x)/(2cos(x))

1/(sin(2x)) = csc(x)/(2cos(x))

1/(2*sin(x)*cos(x)) = csc(x)/(2cos(x))

(1/sin(x))*1/(2*cos(x)) = csc(x)/(2cos(x))

csc(x)*1/(2*cos(x)) = csc(x)/(2cos(x))

csc(x)/(2*cos(x)) = csc(x)/(2cos(x))

The identity is confirmed. Notice how I only altered the left hand side (LHS) keeping the right hand side (RHS) the same each time.

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Answer:

The  width is  w = \$ 729.7

Step-by-step explanation:

From the question we are told that

   The population standard deviation is  \sigma =  \% 1,000

    The  sample size is  n  = 50

    The sample mean  is  \= x  =  \$ 15,000

Given that the confidence level is  99% then the level of significance is mathematically represented as  

               \alpha  =  100 - 99

=>            \alpha  =  1\%

=>             \alpha  = 0.01

Next we obtain the critical value of  \frac{\alpha }{2} from the normal distribution table, the value is

             Z_{\frac{\alpha }{2} } = Z_{\frac{0.01 }{2} } =  2.58

Generally margin of error is mathematically represented as

             E =  Z_{\frac{\alpha }{2} *  \frac{\sigma }{\sqrt{n} }

substituting values

              E = 2.58 *  \frac{1000 }{\sqrt{50} }

              E = 2.58 *  \frac{1000 }{\sqrt{50} }

               E = 364.9

The width of the 99% confidence interval is mathematically evaluated as

         w = 2 * E

substituting values

          w = 2 * 364.9

          w = \$ 729.7

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