What is the general solution for (33)/(sin(x))=(29)/(sin(100)) ?

The general solution for (33)/(sin(x))=(29)/(sin(100)) is No Solution for x\in\mathbb{R}

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(33)/(sin(x))=(29)/(sin(100))

\frac{33}{sin ( x )} = \frac{29}{sin ( 10 0 ^{\circ} )}

No Solution for x \in R

Solution steps

\frac{33}{sin ( x )} = \frac{29}{sin ( 10 0 ^{\circ} )}

Cross multiply

\frac{33}{sin ( x )} = \frac{29}{sin ( 10 0 ^{\circ} )}

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

33 sin (10 0^{\circ}) = sin (x) \cdot 29

33 sin (10 0^{\circ}) = sin (x) \cdot 29

Switch sides

sin (x) \cdot 29 = 33 sin (10 0^{\circ})

Divide both sides by

29

sin (x) \cdot 29 = 33 sin (10 0^{\circ})

Divide both sides by

29

\frac{sin ( x ) \cdot 29}{29} = \frac{33 sin ( 10 0 ^{\circ} )}{29}

Simplify

sin (x) = \frac{33 sin ( 10 0 ^{\circ} )}{29}

sin (x) = \frac{33 sin ( 10 0 ^{\circ} )}{29}

Verify Solutions

Find undefined (singularity) points:

sin (x) = 0

Take the denominator(s) of

\frac{33}{sin ( x )}

and compare to zero

sin (x) = 0

The following points are undefined

sin (x) = 0

Combine undefined points with solutions:

sin (x) = \frac{33 sin ( 10 0 ^{\circ} )}{29}

- 1 \leq sin (x) \leq 1

No Solution for x \in R

2 cos^{2} (x) - 1 = sin (x)

(\frac{1}{2}) = cos (θ)

sin (θ) = \frac{4}{5}, θ, I, cos (2 θ)

sec^{2} (x) cot (x) = 4

1 = 4 cos (2 θ)

What is the general solution for (33)/(sin(x))=(29)/(sin(100)) ?
The general solution for (33)/(sin(x))=(29)/(sin(100)) is No Solution for x\in\mathbb{R}