What is the general solution for sin(x)=cos(2x+10) ?

The general solution for sin(x)=cos(2x+10) is x=(pi-20+4pin)/6 ,x=-(pi+20+4pin)/2

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sin(x)=cos(2x+10)

sin (x) = cos (2 x + 10)

x = \frac{π - 20 + 4 πn}{6}, x = - \frac{π + 20 + 4 πn}{2}

Solution steps

sin (x) = cos (2 x + 10)

Rewrite using trig identities

sin (x) = sin (\frac{π}{2} - (2 x + 10))

Apply trig inverse properties

x = \frac{π}{2} - (2 x + 10) + 2 πn, x = π - (\frac{π}{2} - (2 x + 10)) + 2 πn

x = \frac{π}{2} - (2 x + 10) + 2 πn : x = \frac{π - 20 + 4 πn}{6}

x = π - (\frac{π}{2} - (2 x + 10)) + 2 πn : x = - \frac{π + 20 + 4 πn}{2}

x = \frac{π - 20 + 4 πn}{6}, x = - \frac{π + 20 + 4 πn}{2}

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

6 cos (x) = - 6 (1 + cos (x))

sin (θ) = \frac{60 sin ( 1 5 ^{\circ} )}{400}

sin^{2} (x) - 3 cos (x) - 1 = 0

2 cos^{2} (θ) + 2 cos (θ) = 0

What is the general solution for sin(x)=cos(2x+10) ?
The general solution for sin(x)=cos(2x+10) is x=(pi-20+4pin)/6 ,x=-(pi+20+4pin)/2