Processing Math: Done

From Förberedande kurs i matematik 1

If we use the formula for double angles, sin 2x=2sin x cos x, and move all the terms over to the left-hand side, the equation becomes

2sinxcosx−2cosx=0 

Then, we see that we can take a factor cos x out of both terms,

cosx2sinx−2=0 

and hence divide up the equation into two cases. The equation is satisfied either if cos x=0 or if 2sinx−2=0 .

cos x=0 : this equation has the general solution

x=2+n ( n an arbitrary integer)

2sinx−2=0 : If we collect sin x on the left-hand side, we obtain the equation sin x =12 , which has the general solution

x=4+2nx=43+2n  ( n an arbitrary integer)

The complete solution of the equation is

x=4+2nx=2+nx=43+2n ( n an arbitrary integer).