What is the general solution for sin(x)*cos^2(x)=sin(x) ?

The general solution for sin(x)*cos^2(x)=sin(x) is x=2pin,x=pi+2pin

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sin(x)*cos^2(x)=sin(x)

sin (x) \cdot cos^{2} (x) = sin (x)

x = 2 πn, x = π + 2 πn

Solution steps

sin (x) cos^{2} (x) = sin (x)

Subtract

sin (x)

from both sides

cos^{2} (x) sin (x) - sin (x) = 0

Factor

cos^{2} (x) sin (x) - sin (x) : sin (x) (cos (x) + 1) (cos (x) - 1)

sin (x) (cos (x) + 1) (cos (x) - 1) = 0

Solving each part separately

sin (x) = 0 or cos (x) + 1 = 0 or cos (x) - 1 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

cos (x) + 1 = 0 : x = π + 2 πn

cos (x) - 1 = 0 : x = 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn

sinh (y) = - 2

2 sin (θ) = - 3 + 4 sin (θ)

7^{2} = 6^{2} + 1 1^{2} - 2 \cdot 6 \cdot 11 \cdot cos (D)

- 4 cos^{2} (x) + 3 cos (x) + 1 = 0

cos^{2} (θ) + \frac{5 ^{2} cos ( θ )}{9.81 ( 8 )} - 1 = 0

What is the general solution for sin(x)*cos^2(x)=sin(x) ?
The general solution for sin(x)*cos^2(x)=sin(x) is x=2pin,x=pi+2pin