What is the general solution for 0.5=sin(x)cos(x) ?

The general solution for 0.5=sin(x)cos(x) is x= pi/4+pin

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0.5=sin(x)cos(x)

0.5 = sin (x) cos (x)

x = \frac{π}{4} + πn

Solution steps

0.5 = sin (x) cos (x)

Switch sides

sin (x) cos (x) = 0.5

Rewrite using trig identities

\frac{sin ( 2 x )}{2} = 0.5

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

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

tan^{2} (θ) + sec (θ) = - 2

9 csc (x) = 63

sin (x) (cos (x) + 1) = 0

1 5^{2} = 1 2^{2} + 2 0^{2} - 2 \cdot 12 \cdot 20 \cdot cos (a)

What is the general solution for 0.5=sin(x)cos(x) ?
The general solution for 0.5=sin(x)cos(x) is x= pi/4+pin