trig
posted by Anonymous on .
how to do the calculation while taking 'A'
as 15 in the half angle formula used for calculating the value of sin 7.5 ?

Unless you have found sin15 or cos15 before, and it has become part of your trig repertoire , you will have to do it twice
since you must know that cos 30 = √3/2
and using
cos 2A = 2cos^2 A  1 , let 2A = 30
cos30 = 2cos^2 15  1
solving this for cos 15 I got √(√3 + 2)/2
now use the other expansion for cos 2A
cos 2A = 1  2sin^2 A
cos 15 = 1  2sin^2 7.5
this gave me
2sin^2 7.5 = 1  √(√3 + 2)/2
sin 7.5 = √[2  √(√3 + 2) ]/2
you can check it with sin 7.5 on your calculator, it is correct.