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

The general solution for 4sin(x)cos(x)=1 is x= pi/(12)+pin,x=(5pi)/(12)+pin

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4sin(x)cos(x)=1

4 sin (x) cos (x) = 1

x = \frac{π}{12} + πn, x = \frac{5 π}{12} + πn

Solution steps

4 sin (x) cos (x) = 1

Rewrite using trig identities

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Divide the numbers:

\frac{4}{2} = 2

2 sin (2 x) = 1

Divide both sides by

2

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

General solutions for

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

2 x = \frac{π}{6} + 2 πn, 2 x = \frac{5 π}{6} + 2 πn

Solve

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

Solve

2 x = \frac{5 π}{6} + 2 πn : x = \frac{5 π}{12} + πn

x = \frac{π}{12} + πn, x = \frac{5 π}{12} + πn

sec^{2} (x) - sec (x) = 2

sin (x) = \frac{4}{5}

4 sin^{2} (θ) = 3 cos^{2} (θ), 0^{\circ} < θ < 36 0^{\circ}

2 sin (x) - 2 = 0

tan (θ) = \frac{1}{2}

What is the general solution for 4sin(x)cos(x)=1 ?
The general solution for 4sin(x)cos(x)=1 is x= pi/(12)+pin,x=(5pi)/(12)+pin