00:01
Hello, the question is taken from trigonometry and the question is find the exact value of sine cosine and tangent of the angle.
00:08
Okay, so let me evaluate this value.
00:12
Sign of 2 pi by 3 minus 9 pi by 4.
00:22
That is equal to using the formula of sine of a minus b.
00:26
We know that this is equal to sine a, sine cos b minus core.
00:35
A sign b okay so this will give you the value sign 2 pi by 3 is sign pi minus pi by 3 so that is sine 180 minus theta that is sign theta which is sine pi by 3 course 2 pi by theta 2 pi plus theta is cos theta pose pi by 4 minus minus so this will be cos by 3 and sign by sine pi by 3 is equal to square root 3 by 2 course pi by 4 1 by square 2 plus 1 by 2 2 so this value is square 3 plus 1 over 2 2 now we need to evaluate course 2 pi by 3 minus 9 pi by 4 we know that course theta is squared 1 minus sine square theta sine square 2 pi by 3 minus 9 pi by 4 let us solve it so sine square 2 pi by 3 minus 9 pi by 4 is equal to square root 3 plus 1 whole square over 8 so this will be 3 plus 1 plus 2 root 3 over 8 so this will be 1 by 2 plus square out 3 over 4.
02:08
Okay, substituting this value we get this value in the equation, we get square root 1 minus 1 by 2 minus square root 3 by 4.
02:27
So that will be equal to square root 1 by 2 minus square root 3 by 4...