Solve cosa/1-tana+sina/1-cota=sina+cosa

Evaluate

\frac{cos ( a )}{1} - tan (a) + \frac{sin ( a )}{1} - cot (a) = sin (a) + cos (a)

Divide the terms

cos (a) - tan (a) + \frac{sin ( a )}{1} - cot (a) = sin (a) + cos (a)

Cancel equal terms on both sides of the expression

- tan (a) + \frac{sin ( a )}{1} - cot (a) = sin (a)

Divide the terms

- tan (a) + sin (a) - cot (a) = sin (a)

Cancel equal terms on both sides of the expression

- tan (a) - cot (a) = 0

Rewrite the expression

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

Multiply both sides of the equation by LCD

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

Simplify the equation

More Steps

- sin^{2} (a) - cos^{2} (a) = 0 \times cos (a) sin (a)

Any expression multiplied by 0 equals 0

- sin^{2} (a) - cos^{2} (a) = 0

Divide both sides

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

Divide the terms

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

Rewrite the expression

- tan^{2} (a) - 1 = 0

Solution

a \in / R

Alternative Form

No real solution

Solve the equation