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

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

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sin(x)cos(x)=1

sin (x) cos (x) = 1

No Solution for x \in R

Solution steps

sin (x) cos (x) = 1

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} = 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

csc^{2} (x) = 2

6 sec^{2} (θ) tan (θ) = 8 tan (θ)

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

cot (2 x) = 3

sin^{2} (θ) = 5 (cos (θ) + 1)

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