Solve cota-1/2-sec^2a=cota/1+tana

Question

Solve the equation

a \in / R

Alternative Form

No real solution

Evaluate

cot (a) - \frac{1}{2} - sec^{2} (a) = \frac{cot ( a )}{1} + tan (a)

Divide the terms

cot (a) - \frac{1}{2} - sec^{2} (a) = cot (a) + tan (a)

Cancel equal terms on both sides of the expression

- \frac{1}{2} - sec^{2} (a) = tan (a)

Use sec^{2} (x) = tan^{2} (x) + 1 to rewrite the expression

- \frac{3}{2} - tan^{2} (a) = tan (a)

Move the expression to the left side

- \frac{3}{2} - tan^{2} (a) - tan (a) = 0

Rewrite in standard form

- tan^{2} (a) - tan (a) - \frac{3}{2} = 0

Multiply both sides

tan^{2} (a) + tan (a) + \frac{3}{2} = 0

Multiply both sides

2 (tan^{2} (a) + tan (a) + \frac{3}{2}) = 2 \times 0

Calculate

2 tan^{2} (a) + 2 tan (a) + 3 = 0

Substitute a= 2,b= 2 and c= 3 into the quadratic formula tan (a) = \frac{- b \pm b ^{2} - 4 a c}{2 a}

tan (a) = \frac{- 2 \pm 2 ^{2} - 4 \times 2 \times 3}{2 \times 2}

Simplify the expression

tan (a) = \frac{- 2 \pm 2 ^{2} - 4 \times 2 \times 3}{4}

Simplify the expression

More Steps

tan (a) = \frac{- 2 \pm - 20}{4}

Simplify the radical expression

More Steps

tan (a) = \frac{- 2 \pm 2 5 \times i}{4}

Separate the equation into 2 possible cases

tan (a) = \frac{- 2 + 2 5 \times i}{4} tan (a) = \frac{- 2 - 2 5 \times i}{4}

Simplify the expression

More Steps

tan (a) = - \frac{1}{2} + \frac{5}{2} i tan (a) = \frac{- 2 - 2 5 \times i}{4}

Simplify the expression

More Steps

tan (a) = - \frac{1}{2} + \frac{5}{2} i tan (a) = - \frac{1}{2} - \frac{5}{2} i

Rearrange the terms

a \in / R a \in / R

Solution

a \in / R

Alternative Form

No real solution

Show Solution