What is the general solution for cot(a)sec(a)=cos(a) ?

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

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cot(a)sec(a)=cos(a)

cot (a) sec (a) = cos (a)

No Solution for a \in R

Solution steps

cot (a) sec (a) = cos (a)

Subtract

cos (a)

from both sides

cot (a) sec (a) - cos (a) = 0

Express with sin, cos

\frac{1 - cos ( a ) sin ( a )}{sin ( a )} = 0

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

1 - cos (a) sin (a) = 0

Rewrite using trig identities

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

Move

1

to the right side

- \frac{sin ( 2 a )}{2} = - 1

Multiply both sides by

2

- sin (2 a) = - 2

Divide both sides by

- 1

sin (2 a) = 2

- 1 \leq sin (x) \leq 1

No Solution for a \in R

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

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

2 tan^{2} (x) + 3 tan (x) - 2 = 0

sin^{2} (2 x) - \frac{1}{2 3} sin (4 x) = \frac{1}{2}

x, sin (x + x y) = 0

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