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

The general solution for (cos(x))(sin(x))=-1 is No Solution for x\in\mathbb{R}

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(cos(x))(sin(x))=-1

(cos (x)) (sin (x)) = - 1

No Solution for x \in R

Solution steps

(cos (x)) (sin (x)) = - 1

Rewrite using trig identities

cos (x) sin (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} = - 1

Multiply both sides by

2

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

Multiply both sides by

2

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

Simplify

sin (2 x) = - 2

sin (2 x) = - 2

- 1 \leq sin (x) \leq 1

No Solution for x \in R

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

2 - sin (x) = sin (x)

cos^{2} (t) = \frac{1}{2}

2 cos^{2} (θ) - 1 = sin (θ), 0^{\circ} \leq θ \leq 18 0^{\circ}

x, e^{c o s (x)} (1 - cos (y)) = c

What is the general solution for (cos(x))(sin(x))=-1 ?
The general solution for (cos(x))(sin(x))=-1 is No Solution for x\in\mathbb{R}