Solve for x:
1-2 cos^2(x)+cos^4(x)+2 sin^2(x)-cos(x) sin(x) sin(2 x) = 0
Reduce trigonometric functions:
-3/8 (-3+4 cos(2 x)-cos(4 x)) = 0
Multiply both sides by -8/3:
-3+4 cos(2 x)-cos(4 x) = 0
Transform -3+4 cos(2 x)-cos(4 x) into a polynomial with respect to cos(2 x) using cos(4 x) = 2 cos^2(2 x)-1:
-2+4 cos(2 x)-2 cos^2(2 x) = 0
Divide both sides by -2:
1-2 cos(2 x)+cos^2(2 x) = 0
Write the left hand side as a square:
(cos(2 x)-1)^2 = 0
Take the square root of both sides:
cos(2 x)-1 = 0
Add 1 to both sides:
cos(2 x) = 1
Take the inverse cosine of both sides:
2 x = 2 π n for n element Z
Divide both sides by 2:
Answer: |x = π n for n element Z
Solve for x:
1-2 cos^2(x)+cos^4(x)+2 sin^2(x)-cos(x) sin(x) sin(2 x) = 0
Reduce trigonometric functions:
-3/8 (-3+4 cos(2 x)-cos(4 x)) = 0
Multiply both sides by -8/3:
-3+4 cos(2 x)-cos(4 x) = 0
Transform -3+4 cos(2 x)-cos(4 x) into a polynomial with respect to cos(2 x) using cos(4 x) = 2 cos^2(2 x)-1:
-2+4 cos(2 x)-2 cos^2(2 x) = 0
Divide both sides by -2:
1-2 cos(2 x)+cos^2(2 x) = 0
Write the left hand side as a square:
(cos(2 x)-1)^2 = 0
Take the square root of both sides:
cos(2 x)-1 = 0
Add 1 to both sides:
cos(2 x) = 1
Take the inverse cosine of both sides:
2 x = 2 π n for n element Z
Divide both sides by 2:
Answer: |x = π n for n element Z
No wonder you gave me a 1 star guys, I made a mistake
The correct equation is: cos4x−(sin2x)(sinx)(cosx)−2cos2x+sin4x+2sin2x+1=0
Hi Max :)
\cos^4x-(\sin 2x)(\sin x)(\cos x)-2\cos^2x+\sin^4x+2\sin^2x+1=0
cos4x−(sin2x)(sinx)(cosx)−2cos2x+sin4x+2sin2x+1=0cos4x+sin4x−(sin2x)(sin2x2)−2(cos2x−sin2x)+1=0cos4x+sin4x+2cox2xsin2x−2cox2xsin2x−(sin2x)(sin2x2)−2(cos2x)+1=0(cos2x+sin2x)2−4cox2xsin2x2−(sin2x)(sin2x2)−2(cos2x)+1=01−(2cosxsinx)22−(sin2x)(sin2x2)−2(cos2x)+1=0−(sin2x)22−(sin2x)22−2(cos2x)+2=0−(sin2x)2−2(cos2x)+2=0−[1−cos2(2x)]−2(cos2x)+2=0−1+(cos2x)2−2(cos2x)+2=0(cos2x)2−2(cos2x)+1=0lety=cos2xy2−2y+1=0(y−1)2=0y=1cos2x=12x=2πnn∈Zx=πnn∈Z
check
cos4(2πn)−(sin2∗(2πn))(sin(2πn))(cos(2πn))−2cos2(2πn)+sin4(2πn)+2sin2(2πn)+1=01−0−2+0+0+1=0GOOD