What is the general solution for sin(x)cos(x)=(sqrt(3))/4 ?

The general solution for sin(x)cos(x)=(sqrt(3))/4 is x= pi/6+pin,x= pi/3+pin

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sin(x)cos(x)=(sqrt(3))/4

sin (x) cos (x) = \frac{3}{4}

x = \frac{π}{6} + πn, x = \frac{π}{3} + πn

Solution steps

sin (x) cos (x) = \frac{3}{4}

Rewrite using trig identities

\frac{sin ( 2 x )}{2} = \frac{3}{4}

Multiply both sides by

2

sin (2 x) = \frac{3}{2}

General solutions for

sin (2 x) = \frac{3}{2}

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

Solve

2 x = \frac{π}{3} + 2 πn : x = \frac{π}{6} + πn

Solve

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

x = \frac{π}{6} + πn, x = \frac{π}{3} + πn

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

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

2 sin (x) + cos (2 x) = 1

2 sin (2 x) = 0

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

What is the general solution for sin(x)cos(x)=(sqrt(3))/4 ?
The general solution for sin(x)cos(x)=(sqrt(3))/4 is x= pi/6+pin,x= pi/3+pin