00:01
In this problem today, we are asked to find all solutions of the following equation.
00:24
What is the equation? sin x times cos 2x plus x times sine 2x equal to 1.
00:49
And the range is given as the semi -closed interval of 0 to 2 -pil.
01:00
So how do we solve this? trigramometric equation.
01:10
Now we have sine x cost 2x plus x, sine 2x equal to 1.
01:35
Therefore, from trigonometric identity, we have sine x plus 2x equal to 1 on sine 3x equal 1.
01:57
We are also given this range, the semi -closed interval 0 to 2 -5.
02:03
If x belongs, then 2 times x will belong to the semi -closed interval 0 to 6 -5.
02:27
Now we have this equation, times 3x equal to 1.
02:33
So let us term this number 1, or equation 1.
02:37
From equation 1, we have 3x equal to pi by 2, and then again, it will be 1 again in the first quadrant.
02:59
So 5, sorry, it is not pi by 2, it is pi over 2, or pi by 2 as we say normally...