2015-11-03 16:23:03
Im learning trigonometric equations, and we learn them according to types. For example we learnt how to solve all equations in ype cosx=x, or tan(f(x))=cot(f(x)) and others according to steps and which identities to use and its helpfull and the only way i can learn it. But I was sick for a while and missed alot. Anyway, how do I solve step by step equasions like this? Thanks! Sinx+cosx=a /sinx-cosx=a
2015-11-03 22:32:59

Show both sides equal, you can choose to square both sides (modulus takes care of a=-a type) and expand both sides for equality. in(x) + cos(x) = a  [sin(x) + cos(x)][sin(x) - cos(x)] = sin2x - cos2x  Use trigonometric identity:  cos(2x) = cos2x - sin2x  sin2x - cos2x = -cos(2x)  Therefore,  [sin(x) + cos(x)][sin(x) - cos(x)] = -cos(2x)  a [sin(x) - cos(x)] = -cos(2x)  sin(x) - cos(x) = -(1/a) cos(2x)  |sin(x) - cos(x)| = |(1/a) cos(2x)|