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

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

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cos(θ)-sin(θ)=cot(θ)cos(θ)

cos (θ) - sin (θ) = cot (θ) cos (θ)

No Solution for θ \in R

Solution steps

cos (θ) - sin (θ) = cot (θ) cos (θ)

Subtract

cot (θ) cos (θ)

from both sides

cos (θ) - sin (θ) - cot (θ) cos (θ) = 0

Express with sin, cos

\frac{- cos ^{2} ( θ ) - sin ^{2} ( θ ) + cos ( θ ) sin ( θ )}{sin ( θ )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

- cos^{2} (θ) - sin^{2} (θ) + cos (θ) sin (θ) = 0

Rewrite using trig identities

- 1 + \frac{sin ( 2 θ )}{2} = 0

Move

1

to the right side

\frac{sin ( 2 θ )}{2} = 1

Multiply both sides by

2

sin (2 θ) = 2

- 1 \leq sin (x) \leq 1

No Solution for θ \in R

- 2 tan (x) + 1 + 2 tan^{2} (x) = tan^{2} (x)

\frac{sin ( a )}{50} = \frac{sin ( 2 5 ^{\circ} )}{35}

sin (x + \frac{π}{4}) = \pm 1

sin (2 x + 64) = \frac{3}{2}

sin (θ) = 0, 6

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