What is the general solution for sin(x)cos(x)=3 ?

The general solution for sin(x)cos(x)=3 is No Solution for x\in\mathbb{R}

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sin(x)cos(x)=3

sin (x) cos (x) = 3

No Solution for x \in R

Solution steps

sin (x) cos (x) = 3

Rewrite using trig identities

sin (x) cos (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 x )}{2}

\frac{sin ( 2 x )}{2} = 3

Multiply both sides by

2

\frac{sin ( 2 x )}{2} = 3

Multiply both sides by

2

\frac{2 sin ( 2 x )}{2} = 3 \cdot 2

Simplify

sin (2 x) = 6

sin (2 x) = 6

- 1 \leq sin (x) \leq 1

No Solution for x \in R

- 2 cos^{2} (4 x) + 2 sin (4 x) - 1 = 0

cos (θ) = \frac{75}{10}

tan (x) = \frac{50}{30}

cos^{(2)} (x) + 2 cos (x) = 3

cos (A) = \frac{1 ^{2} + 5. 2 ^{2} - 3.5}{2 ( 1 ) ( 5.2 )}

What is the general solution for sin(x)cos(x)=3 ?
The general solution for sin(x)cos(x)=3 is No Solution for x\in\mathbb{R}