
The given pair of angles are vertical opposite angle pair so, they are equal. i.e
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.
Answer: 97.72%
Step-by-step explanation:
Given : A shoe manufacturer collected data regarding men's shoe sizes and found that the distribution of sizes exactly fits the normal curve.
Let x be the random variable that represents the shoe sizees.
Also, The population mean =
; Standard deviation: 
Formula for z:-

Put x= 8, we get

Now, the probability that the male shoe sizes are greater than 8 :-

Hence, the percent of male shoe sizes are greater than 8 is 97.72%.
The answer would be 7776^2 / 343^2 written as a fraction OR about 513.95402 written as a decimal.