find all solutions, 1-tan^2(3x)=0?

Answer 1

Moving things about, we have Tan^2(3x)=1, which gives us Tan(3x)=+/- 1. From inspection, solutions of 3x are +/- (pi/4, 3pi/4, 5 pi/4 , [2n-1] pi/4, ..........n= 1 to infinity
So solutions of x are +/- (pi/12, pi/4, 5pi/12, .....

Answer 2

So, tan^2(3x) = 1

Therefore tan(3x) = 1 or tan(3x) = -1. We will find solutions within one 360 degree revolution. Adding or subtracting multiples of 360 will also be solutions. So,

Take the first possibility. Then 3x = 45 (angles in degrees, you can easily apply the same reasoning in radians) or 3x = 225. Then in this case x =15 degrees, or x = 75 degrees.

Take the second case. Then 3x = 135 or 3x = 315. Then in this case x = 45 or x = 105.

So all solutions in degrees for x are 15, 45, 75, and 105 or any of these plus or minus 360 degrees.

Answer 3

1-tan^2 3x = 0
<=> tan^2 3x = 1
<=> tan 3x = ±1
<=> 3x = (2k+1)π/4, k ∈ Z
<=> x = (2k+1)π/12, k ∈ Z.

Answer 4

tan^2(3x)= 1 so tan(3x)=+-1
for tan 3x = 1 we get 3x= pi/4 +kpi so
x=pi/12+kpi/3 K any integer
For tan(3x)=-1 we get 3x=3pi/4+kpi s
x=pi/4+kpi/3