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

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

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sin(z)*cos(z)=1

sin (z) \cdot cos (z) = 1

No Solution for z \in R

Solution steps

sin (z) cos (z) = 1

Rewrite using trig identities

sin (z) cos (z)

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 z )}{2}

\frac{sin ( 2 z )}{2} = 1

Multiply both sides by

2

\frac{sin ( 2 z )}{2} = 1

Multiply both sides by

2

\frac{2 sin ( 2 z )}{2} = 1 \cdot 2

Simplify

sin (2 z) = 2

sin (2 z) = 2

- 1 \leq sin (x) \leq 1

No Solution for z \in R

0 = 2 cos (x)

\frac{cos ( x )}{cos ( x )} = \frac{cos ( x )}{1 + sin ( x )}

- 2 cos (θ) - 3 = 0

4 cos^{2} (2 x) = 1

sec (x) = - 4.5973

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