What is the general solution for sin(pi-x)=cos((3pi)/2-x)+cos(pi) ?

The general solution for sin(pi-x)=cos((3pi)/2-x)+cos(pi) is x=(7pi)/6+2pin,x=(11pi)/6+2pin

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sin(pi-x)=cos((3pi)/2-x)+cos(pi)

sin (π - x) = cos (\frac{3 π}{2} - x) + cos (π)

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Solution steps

sin (π - x) = cos (\frac{3 π}{2} - x) + cos (π)

cos (π) = - 1

sin (π - x) = cos (\frac{3 π}{2} - x) + - 1

Rewrite using trig identities

sin (x) = - sin (x) - 1

Subtract

- sin (x) - 1

from both sides

2 sin (x) + 1 = 0

Move

1

to the right side

2 sin (x) = - 1

Divide both sides by

2

sin (x) = - \frac{1}{2}

General solutions for

sin (x) = - \frac{1}{2}

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

4 csc (x) + 8 = 0

2 cos (2 θ) + 3 = 2

sin (\frac{3 π}{2} - 2 x) = sin (x)

α, sin (α) - sin (β) = cos (β) - cos (α)

- \frac{6}{7} = tan (t)

What is the general solution for sin(pi-x)=cos((3pi)/2-x)+cos(pi) ?
The general solution for sin(pi-x)=cos((3pi)/2-x)+cos(pi) is x=(7pi)/6+2pin,x=(11pi)/6+2pin