Question

solve the following equation cos m theta =cos n theta​

Answer 1

Answer:

i think your solution's good. It doesn't get much 'simpler' I believe. Perhaps the presentation could be made better. We have that

sin(y)=x⟺y=(−1)karcsin(x)+kπ

for some k∈Z. Hence, from cos(nθ)=sin(π/2−nθ) we have that

sin(mθ)=cos(nθ)⟺mθ=(−1)k(π/2−nθ)+kπ⟺(m+(−1)kn)θ=(k+(−1)k2)π⟺θ=(2k+(−1)km+(−1)kn)π2