What is the general solution for (sin^3(x))/(sin(x))=0 ?

The general solution for (sin^3(x))/(sin(x))=0 is No Solution for x\in\mathbb{R}

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(sin^3(x))/(sin(x))=0

\frac{sin ^{3} ( x )}{sin ( x )} = 0

No Solution for x \in R

Solution steps

\frac{sin ^{3} ( x )}{sin ( x )} = 0

Simplify

\frac{sin ^{3} ( x )}{sin ( x )} : sin^{2} (x)

\frac{sin ^{3} ( x )}{sin ( x )}

Cancel the common factor:

sin (x)

= sin^{2} (x)

sin^{2} (x) = 0

Apply rule

x^{n} = 0 \Rightarrow x = 0

sin (x) = 0

General solutions for

sin (x) = 0

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 2 πn

Solve

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn, x = π + 2 πn

Since the equation is undefined for:

2 πn, π + 2 πn

No Solution for x \in R

sin (135 - x) = sin (x)

tan (x) - 4 = - 1

4 cos^{2} (x) - 8 cos (x) + 3 = 0

sin (2 x) = - 0.6

\frac{11}{sin ( 9 0 ^{\circ} )} = \frac{10}{sin ( x )}

What is the general solution for (sin^3(x))/(sin(x))=0 ?
The general solution for (sin^3(x))/(sin(x))=0 is No Solution for x\in\mathbb{R}