What is the general solution for (csc(b))/(csc(b))= 1/(sqrt(1-sin^2(b))) ?

The general solution for (csc(b))/(csc(b))= 1/(sqrt(1-sin^2(b))) is No Solution for b\in\mathbb{R}

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(csc(b))/(csc(b))= 1/(sqrt(1-sin^2(b)))

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

No Solution for b \in R

Solution steps

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

\frac{csc ( b )}{csc ( b )} = 1

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

Multiply both sides by

1 - sin^{2} (b)

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

Simplify

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

Square both sides:

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

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

Solve

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

sin (b) = 0

Verify Solutions:

sin (b) = 0

True

The solution is

sin (b) = 0

General solutions for

sin (b) = 0

b = 0 + 2 πn, b = π + 2 πn

Solve

b = 0 + 2 πn : b = 2 πn

b = 2 πn, b = π + 2 πn

Since the equation is undefined for:

2 πn, π + 2 πn

No Solution for b \in R

3 sec (4 x) = 2

2 cos (x) - 1 = cos (2 x)

0 = 4 cos (2 θ)

tan^{2} (x) cos (x) = tan^{2} (x)

cos (x) sin (x) = 3 sin (x)

What is the general solution for (csc(b))/(csc(b))= 1/(sqrt(1-sin^2(b))) ?
The general solution for (csc(b))/(csc(b))= 1/(sqrt(1-sin^2(b))) is No Solution for b\in\mathbb{R}