Which of the following is equivalent to the expression below?

Question

Cscxtanx + secx

a. 2sin

b. (tanx sinx+ sinx)/(sinx)

c. 4tanx

d. 2sec

Answer 1

We can rewrite each in terms of sin(x) and cos(x). Recall that csc(x)=1/sin(x), tan(x)=sin(x)/cos(x), and sec(x)=1/cos(x). Therefore,

csc(x)tan(x)+sec(x) = (1/sin(x))(sin(x)/cos(x)) + 1/cos(x)

=1/cos(x) + 1/cos(x) (Cancelling out sin(x) in the denominator and numerator)

=2/cos(x)

=2sec(x)

So the expression is equivalent to 2sec(x).