What is the general solution for 2cot^2(z)+5=7csc(z) ?

The general solution for 2cot^2(z)+5=7csc(z) is z=0.33983…+2pin,z=pi-0.33983…+2pin

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2cot^2(z)+5=7csc(z)

2 cot^{2} (z) + 5 = 7 csc (z)

z = 0.33983 \dots + 2 πn, z = π - 0.33983 \dots + 2 πn

Solution steps

2 cot^{2} (z) + 5 = 7 csc (z)

Subtract

7 csc (z)

from both sides

2 cot^{2} (z) + 5 - 7 csc (z) = 0

Rewrite using trig identities

3 + 2 csc^{2} (z) - 7 csc (z) = 0

Solve by substitution

csc (z) = 3, csc (z) = \frac{1}{2}

csc (z) = 3 : z = arccsc (3) + 2 πn, z = π - arccsc (3) + 2 πn

csc (z) = \frac{1}{2} :

No Solution

Combine all the solutions

z = arccsc (3) + 2 πn, z = π - arccsc (3) + 2 πn

Show solutions in decimal form

z = 0.33983 \dots + 2 πn, z = π - 0.33983 \dots + 2 πn

sin^{2} (x) = 6

sin^{2} (φ) + cos^{2} (φ) = 2

x, y^{2} (2 + sin (x)) = 1

2 = cos (x) + sin (x)

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

What is the general solution for 2cot^2(z)+5=7csc(z) ?
The general solution for 2cot^2(z)+5=7csc(z) is z=0.33983…+2pin,z=pi-0.33983…+2pin