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) \cdot 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} = 1 \cdot 2

Simplify

sin (2 x) = 2

sin (2 x) = 2

- 1 \leq sin (x) \leq 1

No Solution for x \in R

3 tan^{2} (θ) + 2 tan (θ) - 3 = 0

sinh (x) = \frac{1}{2}

sin^{2} (x) \cdot sec (x) = \frac{sin ^{2} ( x )}{cot ( x )}

2 tan (θ) + sin (θ) cos (θ) = 0

sec (x) = \frac{25}{7}

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}