Determine the general solution of

Question

Sin2x=4cos2x

thanks in advance

Answer 1

sin 2x/cos 2x = 4
tan 2x = 4
since tan is +, 2x is in either quads I or III

2x = 75.964° or 2x = 180+75.964 = 255.964°
x = 37.98° or x = 127.98

since the period of tan 2x is 90°

general solution:
x = 37.98 + 90k
x = 127.98 + 90k
since when k=1 we hit 127.98

we can use only x = 37.98 + 90k

I will leave it up to you to set your calculator to radians, if the answer is needed in those units,
you would then add (π/2)k

Answer 2

I love the way the question was answered thanks for the explanation