What is the general solution for sin(2x+4)=cos(46) ?

The general solution for sin(2x+4)=cos(46) is x=(16200n+1980-180)/(90),x=(3060+8100n-90)/(45)

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sin(2x+4)=cos(46)

sin (2 x + 4) = cos (4 6^{\circ})

x = \frac{1620 0 ^{\circ} n + 198 0 ^{\circ} - 180}{90}, x = \frac{306 0 ^{\circ} + 810 0 ^{\circ} n - 90}{45}

Solution steps

sin (2 x + 4) = cos (4 6^{\circ})

Rewrite using trig identities

sin (2 x + 4) = sin (9 0^{\circ} - 4 6^{\circ})

Apply trig inverse properties

2 x + 4 = 9 0^{\circ} - 4 6^{\circ} + 36 0^{\circ} n, 2 x + 4 = 18 0^{\circ} - (9 0^{\circ} - 4 6^{\circ}) + 36 0^{\circ} n

2 x + 4 = 9 0^{\circ} - 4 6^{\circ} + 36 0^{\circ} n : x = \frac{1620 0 ^{\circ} n + 198 0 ^{\circ} - 180}{90}

2 x + 4 = 18 0^{\circ} - (9 0^{\circ} - 4 6^{\circ}) + 36 0^{\circ} n : x = \frac{306 0 ^{\circ} + 810 0 ^{\circ} n - 90}{45}

x = \frac{1620 0 ^{\circ} n + 198 0 ^{\circ} - 180}{90}, x = \frac{306 0 ^{\circ} + 810 0 ^{\circ} n - 90}{45}

52 cos (x) - 10 sin (x) cos (x) = 0

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cos^{2} (x) = \frac{( 8 k - 7 )}{7}

2 cos^{2} (x) - 7 cos (x) = - 3

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

What is the general solution for sin(2x+4)=cos(46) ?
The general solution for sin(2x+4)=cos(46) is x=(16200n+1980-180)/(90),x=(3060+8100n-90)/(45)