SOLUTION: cos15 - cos75 = sin pi/8 sin pi/3 sin pi/4 sin pi/6 How do you solve this? The material I learned does not include radians so, I have no clue where to start. What is the f

cos(15°) = cos(45°-30°)       (1) 


    use the basic formula of Trigonometry  cos(a-b) = cos(a)*cos(b) + sin(a)*sin(b).

    Continue line (1) in this way


cos(15°) = cos(45°-30°) = cos(45°)*cos(30°) + sin(45°)*sin(30°) =  + .    (2)




cos(75°) = cos(45°-30°)       (3) 


    use the basic formula of Trigonometry  cos(a+b) = cos(a)*cos(b) - sin(a)*sin(b).

    Continue line (3) in this way


cos(75°) = cos(45°+30°) = cos(45°)*cos(30°) - sin(45°)*sin(30°) =  - .    (4)



Now, subtract (4) from (2).   You will get


    cos(15°) - cos(75°) = .


Now, you should know that 360° = .


Hence,


 =  = 22.5°;


 =  = 60°;


 =  = 45°;


 =  = 90°.


Next,   = sin(45°).


Hence, the answer to the problem's question is  the third line  .