3 - 3*sin(^4)x - 5cos(^4)x = 0

Question

3 - 3*sin(^4)x - 5cos(^4)x = 0

Answer 1

3-3(1-cos2x)²/4-5(1+cos2x)²/4=0
12-3+6cos2x-3cos²2x-5-10cos2x-5cos²2x=0
-8cos²2x-4cos2x+4=0
2cos²2x+cos2x-1=0
cos2x=a
2a²+a-1=0
D=1+8=9
a1=(-1-3)/4=-1⇒cos2x=-1⇒2x=π+2πn⇒x=π/2+πn,n∈z
a2=(-1+3)/4=1/2⇒cos2x=1/2⇒2x=+-π/3+2πk⇒x=+-π/6+πk,k∈z