Find the exact value of the product sec teta csc teta given that sin teta=3/5 and cos teta =4/5
To find the exact value of the product sec teta csc teta, we first need to find the values of sec teta and csc teta using the given values of sin teta and cos teta.
The formula for sec teta is 1/cos teta, and the formula for csc teta is 1/sin teta.
Given that sin teta = 3/5 and cos teta = 4/5, we can substitute these values into the formulas to find sec teta and csc teta.
sec teta = 1/(cos teta) = 1/(4/5) = 5/4
csc teta = 1/(sin teta) = 1/(3/5) = 5/3
Now we can find the product of sec teta and csc teta:
sec teta * csc teta = (5/4) * (5/3)
To multiply fractions, we simply multiply the numerators (top numbers) together and the denominators (bottom numbers) together:
sec teta * csc teta = (5 * 5) / (4 * 3)
Simplifying the numerator and denominator gives:
sec teta * csc teta = 25 / 12
Therefore, the exact value of the product sec teta csc teta, given sin teta = 3/5 and cos teta = 4/5, is 25/12.