Prove that sin theta cos theta = cot theta is not a trigonometric identify by producing a counterexample

One counterexample is theta = pi/4, because

sin(theta)*cos(theta) = sin(pi/4)*cos(pi/4) = sqrt(2)/2*sqrt(2)/2 = 1/2

while

cot(theta) = cot(pi/4) = cos(pi/4)/sin(pi/4) = (sqrt(2)/2)/(sqrt(2)/2) = 1

After plugging in theta = pi/4, the equation

sin(theta)cos(theta) = cot(theta)

becomes

1/2 = 1

which is a false equation. This is enough to show we do not have an identity.

here is your mark brainliest

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;