Determine the minimum value of a positive integer N, satisfying:

cos 96^{o} + sin 96^{o}
tan 19N^{o} = -----------------
cos 96^{o} - sin 96^{o}

(In reply to

Actual answer -- calculator solution by Charlie)

I did the same , but copied the wrong coefficient (17 instead of 159):

LS= -0.809784 approx.

arctan(19N)= arctan( -0.809784 )=-31^{o} +N*180^{o}

^{This angle should be divisible by 19}

for k=17 it is 3021

LS=RS= -0.809784 approx.

so the answer is N = 3021/19= 159

I was exhausted when I have typed in my answer,- since **I HAVE SPENT A LOT OF TIME **trying to solve it analytically**.**