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

The general solution for sin(2x)cos(2x)=sqrt(2) is No Solution for x\in\mathbb{R}

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

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

No Solution for x \in R

Solution steps

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

Rewrite using trig identities

sin (2 x) cos (2 x)

Use the Double Angle identity:

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

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

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

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

Multiply both sides by

2

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

Multiply both sides by

2

\frac{2 sin ( 2 \cdot 2 x )}{2} = 22

Simplify

sin (2 \cdot 2 x) = 22

sin (2 \cdot 2 x) = 22

- 1 \leq sin (x) \leq 1

No Solution for x \in R

\frac{cos ( t )}{3 cos ( 3 t )} = 0

3 tan (3 x) = 1

x, cos (x) + 3 = - cos (x)

2 cos (2 x) + 1 = 0

3 tan (x - 1) = 4, x \leq 2 π, 0

What is the general solution for sin(2x)cos(2x)=sqrt(2) ?
The general solution for sin(2x)cos(2x)=sqrt(2) is No Solution for x\in\mathbb{R}