Question

Which expression is equivalent to sin Bcsc Bsec B for all values of B for which sin Bcsc Bsec B is defined?

Select the correct answer below:
cot Btan B
cot Bsec B
sec B​

Answer 1

Answer: sec(B), third choice

Recall that csc, which stands for cosecant, is defined as follows

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

it is the reciprocal of the sine function. Multiplying csc(B) and sin(B) together yields 1. This result multiplies with the only thing left, sec(B), to get the final answer.