What is the general solution for cos(θ)sin(θ)=172245 ?

The general solution for cos(θ)sin(θ)=172245 is No Solution for θ\in\mathbb{R}

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cos(θ)sin(θ)=172245

cos (θ) sin (θ) = 172245

No Solution for θ \in R

Solution steps

cos (θ) sin (θ) = 172245

Rewrite using trig identities

cos (θ) sin (θ)

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 θ )}{2}

\frac{sin ( 2 θ )}{2} = 172245

Multiply both sides by

2

\frac{sin ( 2 θ )}{2} = 172245

Multiply both sides by

2

\frac{2 sin ( 2 θ )}{2} = 172245 \cdot 2

Simplify

sin (2 θ) = 344490

sin (2 θ) = 344490

- 1 \leq sin (x) \leq 1

No Solution for θ \in R

sec (b) cot (b) = sin (b)

\frac{37}{sin ( x )} = \frac{30}{sin ( 3 0 ^{\circ} )}

\frac{1}{cos ( θ )} = 1

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

3 tan (x + 4 5^{\circ}) = 3

What is the general solution for cos(θ)sin(θ)=172245 ?
The general solution for cos(θ)sin(θ)=172245 is No Solution for θ\in\mathbb{R}