24 March 2012 08:15
A few further points to consider.........
The text book has not introduced the AS level student to compound angle or double angle identities where this question is presented, so these solutions are 'out of scope' in this context.
However your comment 'sin is not a one-to-one function so sin A = sin B does not imply A = B' has led me to the solution through another route.
sin(5x +y ) = sin(90-y+3x)
Either 5x+y = 90-y+3x or 5x+y = 180-(90-y+3x)
x+y=45 x = 11.25
I suppose the answer on the left is discarded because the solution involves multiple values of x and y.
I would prefer to have seen the question reworded as : " Find the least positive value of the angle x which holds true for any value of angle y for which (5x + y) = cos ( y – 3x).
Anyway, thanks very much for your help, Steven. I will now move onto the next chapter !