What is the general solution for sec(b)cot(b)=sin(b) ?

The general solution for sec(b)cot(b)=sin(b) is No Solution for b\in\mathbb{R}

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

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

No Solution for b \in R

Solution steps

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

Subtract

sin (b)

from both sides

sec (b) cot (b) - sin (b) = 0

Express with sin, cos

\frac{1 - sin ^{2} ( b )}{sin ( b )} = 0

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

1 - sin^{2} (b) = 0

Solve by substitution

sin (b) = 1, sin (b) = - 1

sin (b) = 1 : b = \frac{π}{2} + 2 πn

sin (b) = - 1 : b = \frac{3 π}{2} + 2 πn

Combine all the solutions

b = \frac{π}{2} + 2 πn, b = \frac{3 π}{2} + 2 πn

Since the equation is undefined for:

\frac{π}{2} + 2 πn, \frac{3 π}{2} + 2 πn

No Solution for b \in R

\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

0 = sin (π x)

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