SOLUTION: Please simplify this expression as much as possible using the addition and subtraction formula. csc(9pi/2 - v)

Algebra ->  Trigonometry-basics -> SOLUTION: Please simplify this expression as much as possible using the addition and subtraction formula. csc(9pi/2 - v)       Log On


   

Question 249050: Please simplify this expression as much as possible using the addition and subtraction formula.
csc(9pi/2 - v)



Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
csc%289pi%2F2+-+v%29 Start with the given expression.


1%2F%28sin%289pi%2F2+-+v%29%29 Use the identity csc%28x%29=1%2Fsin%28x%29


1%2F%28sin%289pi%2F2%29cos%28v%29-cos%289pi%2F2%29sin%28v%29%29 Use the identity sin%28x-y%29=sin%28x%29cos%28y%29-cos%28x%29sin%28y%29


1%2F%28%281%29cos%28v%29-%280%29sin%28v%29%29 Evaluate the sine and cosine of 9pi%2F2 to get 1 and 0 respectively (use the unit circle).


1%2F%28cos%28v%29-0%29 Multiply


1%2F%28cos%28v%29%29 Combine like terms.


sec%28v%29 Use the identity 1%2Fcos%28x%29=sec%28x%29


So csc%289pi%2F2+-+v%29=sec%28v%29