Question

Is the work shown in the simplification below correct? explain. csc(t) sec(t) = 1 cos(t) ÷ 1 sin(t) = 1 cos(t) • sin(t) 1 = 1 sin(t) = tan(t)?

Answer 1

E2020 Answer:

No, the simplification is not correct.

Cosecant is the reciprocal of sine, not cosine.

Secant is the reciprocal of cosine, not sine.

The given expression simplifies to cot(t).

Answer 2

Answer:

The work shown in the simplification below is incorrect.

Step-by-step explanation:

To start; we have to know  what csc(t) and sec(t) is.

csc(t) = 1/sin(t)      and    sec(t)= 1/cos(t)

So in the above simplification it was all mixed up, csc(t) was substituted with 1/cos(t) instead of 1/sin(t) and sec(t) was substituted with 1/sin(t) instead of 1/cos(t).

So, we are going to solve it the right way;

csc(t) sec(t) = $\frac{1}{sin(t)}$   ÷   $\frac{1}{cos(t)}$

                   =  $\frac{1}{sin(t)}$   ×   $\frac{cos(t)}{1}$

                    =$\frac{cos(t)}{sin(t)}$

                    = cot(t)

Therefore csc(t) sec(t) = cot(t)   and not tan(t).