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

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

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sin(θ)cos(θ)= 1/2

sin (θ) cos (θ) = \frac{1}{2}

θ = \frac{π}{4} + πn

Solution steps

sin (θ) cos (θ) = \frac{1}{2}

Rewrite using trig identities

\frac{sin ( 2 θ )}{2} = \frac{1}{2}

Multiply both sides by

2

sin (2 θ) = 1

General solutions for

sin (2 θ) = 1

2 θ = \frac{π}{2} + 2 πn

Solve

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

θ = \frac{π}{4} + πn

cos (θ) = \frac{- 3}{2}

sin (x) cos (x) = sin (2 x)

cos (x) = \frac{5}{8}

tan (x) = cos (x)

cot (3 x) = 1

What is the general solution for sin(θ)cos(θ)= 1/2 ?
The general solution for sin(θ)cos(θ)= 1/2 is θ= pi/4+pin