What is the general solution for 8sin(x)cos(x)=sqrt(12) ?

The general solution for 8sin(x)cos(x)=sqrt(12) is x= pi/6+pin,x= pi/3+pin

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8sin(x)cos(x)=sqrt(12)

8 sin (x) cos (x) = 12

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

Solution steps

8 sin (x) cos (x) = 12

Rewrite using trig identities

8 \cdot \frac{sin ( 2 x )}{2} = 12

Simplify

8 \cdot \frac{sin ( 2 x )}{2} : 4 sin (2 x)

Simplify

12 : 23

4 sin (2 x) = 23

Divide both sides by

4

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

cos (x) = \frac{1}{5}

3 tan (3 x) + 1 = 0

2 tan (θ) - 3 = 0

csc^{2} (x) - cot (x) = 1

cos (2 x) - 3 sin (x) = 2

What is the general solution for 8sin(x)cos(x)=sqrt(12) ?
The general solution for 8sin(x)cos(x)=sqrt(12) is x= pi/6+pin,x= pi/3+pin