Respuesta :
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:
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) = [tex]\frac{1}{sin(t)}[/tex] ÷ [tex]\frac{1}{cos(t)}[/tex]
= [tex]\frac{1}{sin(t)}[/tex] × [tex]\frac{cos(t)}{1}[/tex]
=[tex]\frac{cos(t)}{sin(t)}[/tex]
= cot(t)
Therefore csc(t) sec(t) = cot(t) and not tan(t).
