Solve (4/cscx) (1/csc^2x)=(3cscx-9)/csc^2x - ScanMath

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Type your math problem... (4/cscx) (1/csc^2x)=(3cscx-9)/csc^2x

Question

Solve the equation

x = ⎩ ⎨ ⎧ arccsc (\frac{9 + 129}{6}) + 2 kπ - arccsc (\frac{9 + 129}{6}) + π + 2 kπ, k \in Z

Alternative Form

x \approx {17.14117 3^{\circ} + 36 0^{\circ} k 162.85882 7^{\circ} + 36 0^{\circ} k, k \in Z

Alternative Form

x \approx {0.29917 + 2 kπ 2.842423 + 2 kπ, k \in Z

Evaluate

(\frac{4}{csc ( x )}) (\frac{1}{csc ^{2} ( x )}) = \frac{3 csc ( x ) - 9}{csc ^{2} ( x )}

Find the domain

More Steps

(\frac{4}{csc ( x )}) (\frac{1}{csc ^{2} ( x )}) = \frac{3 csc ( x ) - 9}{csc ^{2} ( x )}, x \neq = kπ, k \in Z

Simplify

More Steps

\frac{4}{csc ^{3} ( x )} = \frac{3 csc ( x ) - 9}{csc ^{2} ( x )}

Cross multiply

4 csc^{2} (x) = csc^{3} (x) (3 csc (x) - 9)

Move the expression to the left side

4 csc^{2} (x) - csc^{3} (x) (3 csc (x) - 9) = 0

Factor the expression

More Steps

csc^{2} (x) (4 - 3 csc^{2} (x) + 9 csc (x)) = 0

Separate the equation into 2 possible cases

csc^{2} (x) = 0 4 - 3 csc^{2} (x) + 9 csc (x) = 0

Solve the equation

More Steps

x \in / R 4 - 3 csc^{2} (x) + 9 csc (x) = 0

Solve the equation

More Steps

x \in / R x = ⎩ ⎨ ⎧ arccsc (\frac{9 + 129}{6}) + 2 kπ - arccsc (\frac{9 + 129}{6}) + π + 2 kπ, k \in Z

Find the union

x = ⎩ ⎨ ⎧ arccsc (\frac{9 + 129}{6}) + 2 kπ - arccsc (\frac{9 + 129}{6}) + π + 2 kπ, k \in Z

Check if the solution is in the defined range

x = ⎩ ⎨ ⎧ arccsc (\frac{9 + 129}{6}) + 2 kπ - arccsc (\frac{9 + 129}{6}) + π + 2 kπ, k \in Z, x \neq = kπ, k \in Z

Solution

x = ⎩ ⎨ ⎧ arccsc (\frac{9 + 129}{6}) + 2 kπ - arccsc (\frac{9 + 129}{6}) + π + 2 kπ, k \in Z

Alternative Form

x \approx {17.14117 3^{\circ} + 36 0^{\circ} k 162.85882 7^{\circ} + 36 0^{\circ} k, k \in Z

Alternative Form

x \approx {0.29917 + 2 kπ 2.842423 + 2 kπ, k \in Z

Show Solution

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