2sin(x)-(2-sqrt(2))=sqrt(2)csc(x)

Solution

2 sin (x) - (2 - 2) = 2 csc (x)

x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn, x = \frac{π}{2} + 2 πn

Solution steps

2 sin (x) - (2 - 2) = 2 csc (x)

Subtract

2 csc (x)

from both sides

2 sin (x) - 2 + 2 - 2 csc (x) = 0

Rewrite using trig identities

- 2 + \frac{2}{csc ( x )} + 2 - csc (x) 2 = 0

Solve by substitution

csc (x) = - 2, csc (x) = 1

csc (x) = - 2 : x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

csc (x) = 1 : x = \frac{π}{2} + 2 πn

Combine all the solutions

x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn, x = \frac{π}{2} + 2 πn

5 sin (62.83 x) = - 0.32

6 cos^{2} (θ) - 5 = 6 sin^{2} (θ) + sin (θ)

sin (\frac{1}{3} x) = 0

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

sin (2 x) = - sin (4 x)