00:01
In this problem, we need to find all the solutions of the equation in the interval from 0 to 2 pi.
00:06
We have 10 sex squared x plus 5 tan squared x minus 15.
00:13
This is equal to 0.
00:15
So using the pythagorean identity, sex squared x is equal to 1 plus tan squared x.
00:25
So this is what we get.
00:28
So we have 10 times 1 which is 10 plus 10 tan squared x.
00:32
X plus 5 tans squared x minus 15 is equal to 0.
00:39
So 10 tann squared x plus 5 tan squared x, that's 15 tan squared x.
00:44
10 minus 15, that will be minus 5.
00:47
So we end up with 15 tan squared x is equal to 5.
00:53
And that implies that tan squared x is equal to 5 over 15, which is equal to 1 over 3.
01:01
So that's 1 over the square root of 3 whole squared.
01:07
So we have that tan squared x is equal to tan squared pi over 6, and that is because tan of pi over 6 is equal to 1 over 3...