1. The problem statement, all variables and given/known data The simultaneous equations in x,y (cos a)x - (sin a) y = 2 (sin a)x + (cos a)y = 1 are solvable a) for all values of a in the range 0 < a < pi b) except for one value of a in the range 0 < a < pi c) except for two values of a in the range 0 < a < pi d) except for three values of a in the range 0 < a < pi (NB the range is supposed to include 0, I don't have that character on my keyboard) 2. Relevant equations possibly trig identities though I haven't found a way to use these! otherwise just normal methods for solving simultaneous eq. 3. The attempt at a solution I got as far as: cos a = (1 - x sin a)/y (sub into first eq) x(1 - x sin a)/y - y sin a = 2 (multiply by y) (y^2 sin a) + 2y - x - (x^2 sin a) = 0 sin a = (x-2y) / (y^2 - x^2) which I think tells me that sin a cannot equal zero, as this would involve dividing by zero on the RHS? Although come to think of it I'm not sure it tells me that anyway... and it doesn't tell me anything about other values of a as far as I can tell. Any ideas? Thanks.