Evaluate the following expression.(x ≠ π/2 + πn, where n is a whole number)
A)- 6 tan x
B)6 sec x
C)6 tan x
D)- 6 sec x
E)6 cot x

Question

Evaluate the following expression.(x ≠ π/2 + πn, where n is a whole number) ​  ​
A)- 6 tan x 
B)6 sec x 
C)6 tan x 
D)- 6 sec x 
E)6 cot x

Quizplus · Accepted Answer

The expression can be simplified as follows:
-6cos(x-π/2) = -6(cos(x)cos(π/2) + sin(x)sin(π/2)) = -6sin(x)
Taking the reciprocal of sin(x), we get -6/sin(x) = -6csc(x).
Taking the reciprocal of cos(x), we get 1/cos(x) = sec(x).
Therefore, the expression is equivalent to -6csc(x) or -6/sin(x). Since x ≠ π/2 + πn, sin(x) ≠ 0, so we can simplify further to get -6/(sin(x)) = -6csc(x). Finally, using the identity csc(x) = 1/sin(x), we can see that the expression simplifies to -6sec(x).

Evaluate the Following Expression