okay I'll use a / to represent the fraction and F(x) as the integration sign
F(x)cos(3x)/sin2(3x)dx
U=Sin(3x) ; DU=-(3)Cos(3x)
F(x)-(1/3)DU/U2dx
-1/3F(x)1/U2*DUdx
-1/3F(x)U-2DUdx
(-1/3) [1/(-2+1)] U(-2+1)
(-1/3)[-1]U(-1)
(1/3)U-1
(1/3)sin-1(3x)
Your Answer Is:
F(x)cos(3x)/sin2(3x)=(1/3)sin-1(3x)
Also written as:
1/[3sin-1(3x)] or -1/(3sin3x)
Yes. Except where sin x = 0, because then you would be dividing by zero so the quotient is undefined.
The deriviative of sin2 x + cos2 x is 2 cos x - 2 sin x
(1+cosx)(1-cosx)= 1 +cosx - cosx -cos^2x (where ^2 means squared) = 1-cos^2x = sin^2x (sin squared x)
The answer is 1. sin^2 x cos^2/sin^2 x 1/cos^2 cos^2 will be cancelled =1 sin^2 also will be cancelled=1 1/1 = 1
1
sin cubed + cos cubed (sin + cos)( sin squared - sin.cos + cos squared) (sin + cos)(1 + sin.cos)
Multiply both sides by sin(1-cos) and you lose the denominators and get (sin squared) minus 1+cos times 1-cos. Then multiply out (i.e. expand) 1+cos times 1-cos, which will of course give the difference of two squares: 1 - (cos squared). (because the cross terms cancel out.) (This is diff of 2 squares because 1 is the square of 1.) And so you get (sin squared) - (1 - (cos squared)) = (sin squared) + (cos squared) - 1. Then from basic trig we know that (sin squared) + (cos squared) = 1, so this is 0.
Sin squared, cos squared...you removed the x in the equation.
Sin squared is equal to 1 - cos squared.
sin squared
sin2 + cos2 = 1 So, (1 - 2*cos2)/(sin*cos) = (sin2 + cos2 - 2*cos2)/(sin*cos) = (sin2 - cos2)/(sin*cos) = sin2/(sin*cos) - cos2/(sin*cos) = sin/cos - cos-sin = tan - cot
22
You can use the Pythagorean identity to solve this:(sin theta) squared + (cos theta) squared = 1.
Note that an angle should always be specified - for example, 1 - cos square x. Due to the Pythagorean formula, this can be simplified as sin square x. Note that sin square x is a shortcut of (sin x) squared.
Yes. Except where sin x = 0, because then you would be dividing by zero so the quotient is undefined.
The deriviative of sin2 x + cos2 x is 2 cos x - 2 sin x
(1+cosx)(1-cosx)= 1 +cosx - cosx -cos^2x (where ^2 means squared) = 1-cos^2x = sin^2x (sin squared x)