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

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

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

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

x = \frac{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{π}{2} + 2 πn

Solve

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

x = \frac{π}{4} + πn

cos (x) sin (x) - cos (x) = 0

sin^{2} (θ) = sin (θ)

(7 sin (2 x) + 7 cos (2 x))^{2} = 49

- 1 - tan (x) = sec (x)

5 cos (θ) + 4 = 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= pi/4+pin