What is the general solution for cos^4(x)=cos^4(x)csc(x) ?

The general solution for cos^4(x)=cos^4(x)csc(x) is x= pi/2+2pin,x=(3pi)/2+2pin

Popular >

cos^4(x)=cos^4(x)csc(x)

cos^{4} (x) = cos^{4} (x) csc (x)

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Solution steps

cos^{4} (x) = cos^{4} (x) csc (x)

Subtract

cos^{4} (x) csc (x)

from both sides

cos^{4} (x) - cos^{4} (x) csc (x) = 0

Factor

cos^{4} (x) - cos^{4} (x) csc (x) : - cos^{4} (x) (csc (x) - 1)

- cos^{4} (x) (csc (x) - 1) = 0

Solving each part separately

cos^{4} (x) = 0 or csc (x) - 1 = 0

cos^{4} (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

csc (x) - 1 = 0 : x = \frac{π}{2} + 2 πn

Combine all the solutions

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

tan (θ) - 6 = - 2 - 3 tan (θ)

73500 = 130000 \cdot sin (x) + 0.15 \cdot 130000 \cdot cos (x)

cos (\frac{π}{2} + x) - sin (\frac{π}{2} + x) = 0

tan (θ + 3 2^{\circ}) = cot (θ - 2 0^{\circ})

sin^{3} (x) = sin^{3} (x) cos (x)

What is the general solution for cos^4(x)=cos^4(x)csc(x) ?
The general solution for cos^4(x)=cos^4(x)csc(x) is x= pi/2+2pin,x=(3pi)/2+2pin