Answer: [tex]csc(t)[/tex]
Step-by-step explanation:
Alright, lets get started.
The given expression is given as :
[tex]cot( t) \times sec (t)[/tex]
We know quotient identity as :
[tex]cot(t)=\frac{cos(t)}{sin(t)}[/tex]
Similarly, we know reciprocal identity as :
[tex]sec(t)=\frac{1}{cos(t)}[/tex]
lets plug the value of cot and sec in given expression
[tex]\frac{cos(t)}{sin(t)} \times \frac{1}{cos(t)}[/tex]
cos will be cancelled, remaining will be
[tex]\frac{1}{sin(t)}[/tex]
Using reciprocal identity again, that will equal to :
[tex]csc(t)[/tex] ................... Answer (A)
