What is the general solution for sin(x)cos(x)=-1/2 ?

The general solution for sin(x)cos(x)=-1/2 is x=(3pi)/4+pin

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sin(x)cos(x)=-1/2

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

x = \frac{3 π}{4} + πn

Solution steps

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

Rewrite using trig identities

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

Multiply both sides by

2

sin (2 x) = - 1

General solutions for

sin (2 x) = - 1

2 x = \frac{3 π}{2} + 2 πn

Solve

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

x = \frac{3 π}{4} + πn

tan (x) = \frac{7}{3}

3 = 3 cos (2 θ) + sin (2 θ)

8 sin^{2} (x) = sin (x)

6 cos (x) + 6 sin (x) = 36

3 sin (x) + 1 = 0

What is the general solution for sin(x)cos(x)=-1/2 ?
The general solution for sin(x)cos(x)=-1/2 is x=(3pi)/4+pin