`sin(t)csc(pi/2 - t) = tan(t)` Verfiy the identity.

Expert Answers
mathace eNotes educator| Certified Educator

Verify the identity: `sin(t)csc(pi/2-t)=tan(t)`

Simplify the left side of the equation by using the cofunction identity

csc((pi/2)-t)=sec(t).

`sin(t)sec(t)=tan(t)`

Simplify the left side of the equation by using the reciprocal identity

sec(t)=1/cos(t).

`sin(t)*1/cos(t)=tan(t)`

`sin(t)/cos(t)=tan(t)`

`tan(t)=tan(t)`  

balajia | Student

`sin(t).csc((pi)/2-t) =sin(t).sec(t)`

`=(sin(t))/(cos(t)) = tan(t)`