Question

By writing cos15°in the form cos⁡(A-B)and cos75°in the form cos⁡(A+B), determine the angles A and B.

Answer 1

Yeah, you need to use the sum of cosines and the difference of cosines formulas. We have to pick two values that we know the answer to that add up to 75 degrees as well as 2 values we know that will subtract to 15 degrees. So for 15 degrees, we could say that we know the value of cos60 as well as the value of cos 45. Because of that, use the difference of cosines formula using
cos(60 - 45)
For the 75 degree one, the two angles we know the values of that add up to 75 are 30 and 45. SO using the sum of cosines, we can use this formula and these values:
cos(30+45)
Now it's just knowing the formulas and plugging in the info. These are the formulas:
Difference of Cosines:
\[\cos(a-b) = \cos(a)\cos(b)+\sin(a)\sin(b)\]
Sum of Cosines:
\[\cos(a+b) = \cos(a)\cos(b)-\sin(a)\sin(b)\]
So if you can plug in the correct numbers youll definitely be able to get your answer.

Answer 2

oh ok. tq very much @Psymon

Answer 3

Mhm. Try it out and see what ya get : )

Answer 4

cos(60-45)=cos(60)cos(45) + sin(60)sin(45)