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

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

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2sin(x)cos(x)=1

2 sin (x) cos (x) = 1

x = \frac{π}{4} + πn

Solution steps

2 sin (x) cos (x) = 1

Rewrite using trig identities

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) + 2 sin (x) = 0

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

sec^{2} (x) - 2 tan (x) = 0

2 cos (2 x) + 2 = 0

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

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