What is the general solution for sin(x)+sin^2(x)+cos(x)+cos^2(x)=0 ?

The general solution for sin(x)+sin^2(x)+cos(x)+cos^2(x)=0 is x=2pin+pi,x=2pin+(3pi)/2

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

sin (x) + sin^{2} (x) + cos (x) + cos^{2} (x) = 0

x = 2 πn + π, x = 2 πn + \frac{3 π}{2}

Solution steps

sin (x) + sin^{2} (x) + cos (x) + cos^{2} (x) = 0

Rewrite using trig identities

1 + 2 sin (x + \frac{π}{4}) = 0

Move

1

to the right side

2 sin (x + \frac{π}{4}) = - 1

Divide both sides by

2

sin (x + \frac{π}{4}) = - \frac{2}{2}

General solutions for

sin (x + \frac{π}{4}) = - \frac{2}{2}

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

Solve

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

Solve

x + \frac{π}{4} = \frac{7 π}{4} + 2 πn : x = 2 πn + \frac{3 π}{2}

x = 2 πn + π, x = 2 πn + \frac{3 π}{2}

4 cos^{2} (x) - 4 sin (x) - 1 = 0

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

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

2 cos^{3} (x) = cot^{3} (x)

\frac{1}{( sec ^{2} ( a ) )} + \frac{1}{( cos ^{2} ( a ) )} = 1

What is the general solution for sin(x)+sin^2(x)+cos(x)+cos^2(x)=0 ?
The general solution for sin(x)+sin^2(x)+cos(x)+cos^2(x)=0 is x=2pin+pi,x=2pin+(3pi)/2