What is the general solution for sin(x)cos(x)=-1/4 ?

The general solution for sin(x)cos(x)=-1/4 is x=(7pi)/(12)+pin,x=(11pi)/(12)+pin

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sin(x)cos(x)=-1/4

sin (x) cos (x) = - \frac{1}{4}

x = \frac{7 π}{12} + πn, x = \frac{11 π}{12} + πn

Solution steps

sin (x) cos (x) = - \frac{1}{4}

Rewrite using trig identities

\frac{sin ( 2 x )}{2} = - \frac{1}{4}

Multiply both sides by

2

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

General solutions for

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

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

Solve

2 x = \frac{7 π}{6} + 2 πn : x = \frac{7 π}{12} + πn

Solve

2 x = \frac{11 π}{6} + 2 πn : x = \frac{11 π}{12} + πn

x = \frac{7 π}{12} + πn, x = \frac{11 π}{12} + πn

sec^{2} (θ) - 9 = 0

2 cos^{2} (θ) = 2 - sin (θ)

cos (x + 1) = 0

sec^{2} (x) + tan^{2} (x) = 7

4 cos (x) = 1, 0 \leq x \leq 2 π

What is the general solution for sin(x)cos(x)=-1/4 ?
The general solution for sin(x)cos(x)=-1/4 is x=(7pi)/(12)+pin,x=(11pi)/(12)+pin