SOLUTION: 3. Use sum, difference, double angle, and/or half angle identities to evaluate exactly. Show all work sin(25°)*cos(35°)+cos(25°)*sin(35°)

Algebra ->  Trigonometry-basics -> SOLUTION: 3. Use sum, difference, double angle, and/or half angle identities to evaluate exactly. Show all work sin(25°)*cos(35°)+cos(25°)*sin(35°)       Log On


   

Question 746558: 3. Use sum, difference, double angle, and/or half angle identities to evaluate exactly. Show all work
sin(25°)*cos(35°)+cos(25°)*sin(35°)


Answer by KMST(5397) About Me  (Show Source):
You can put this solution on YOUR website!
You must have been taught about trigonometric identities for sum of angles, difference, double angle, and/or half angle.
One of those identities is
sin+%28A%2BB%29=sin%28A%29%2Acos%28B%29%2Bcos%28A%29%2Asin%28B%29
If you replace A=25%5Eo and B=35%5Eo you get

where the right hand side is the expression you have to evaluate.
Since 25%5Eo%2B35%5Eo=60%5Eo we can substitute to get
sin%2860%5Eo%29=ssin%2825%5Eo%29%2Acos%2835%5Eo%29%2Bcos%2825%5Eo%29%2Asin%2835%5Eo%29 or
sin%2825%5Eo%29%2Acos%2835%5Eo%29%2Bcos%2825%5Eo%29%2Asin%2835%5Eo%29=sin%2860%5Eo%29
You should know that the exact value of sin+%2860%5Eo%29 is sqrt%283%29%2F2
so