What is the general solution for solvefor y,-1/2 cot(y)=(t^2)/(+2)+C ?

The general solution for solvefor y,-1/2 cot(y)=(t^2)/(+2)+C is y=arccot(-t^2-2C)+pin

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solvefor y,-1/2 cot(y)=(t^2)/(+2)+C

solve for

y, - \frac{1}{2} cot (y) = \frac{t ^{2}}{+ 2} + C

y = arccot (- t^{2} - 2 C) + πn

Solution steps

- \frac{1}{2} cot (y) = \frac{t ^{2}}{2} + C

Multiply both sides by

- 2

- \frac{1}{2} cot (y) = \frac{t ^{2}}{2} + C

Multiply both sides by

- 2

(- \frac{1}{2} cot (y)) (- 2) = \frac{t ^{2}}{2} (- 2) + C (- 2)

Simplify

(- \frac{1}{2} cot (y)) (- 2) = \frac{t ^{2}}{2} (- 2) + C (- 2)

Simplify

(- \frac{1}{2} cot (y)) (- 2) : cot (y)

(- \frac{1}{2} cot (y)) (- 2)

Remove parentheses:

(- a) = - a, - (- a) = a

= \frac{1}{2} cot (y) \cdot 2

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 2}{2} cot (y)

Cancel the common factor:

2

= cot (y) \cdot 1

Multiply:

cot (y) \cdot 1 = cot (y)

= cot (y)

Simplify

\frac{t ^{2}}{2} (- 2) + C (- 2) : - t^{2} - 2 C

\frac{t ^{2}}{2} (- 2) + C (- 2)

Remove parentheses:

(- a) = - a

= - \frac{t ^{2}}{2} \cdot 2 - C \cdot 2

\frac{t ^{2}}{2} \cdot 2 = t^{2}

\frac{t ^{2}}{2} \cdot 2

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{t ^{2} \cdot 2}{2}

Cancel the common factor:

2

= t^{2}

= - t^{2} - 2 C

cot (y) = - t^{2} - 2 C

cot (y) = - t^{2} - 2 C

cot (y) = - t^{2} - 2 C

Apply trig inverse properties

cot (y) = - t^{2} - 2 C

General solutions for

cot (y) = - t^{2} - 2 C

cot (x) = a \Rightarrow x = arccot (a) + πn

y = arccot (- t^{2} - 2 C) + πn

y = arccot (- t^{2} - 2 C) + πn

3 sec (2 θ) + 2 = 0

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

cos (3 x + 6 0^{\circ}) = 0

2 sin^{2} (x) + (- 2 - 2) sin (x) + 2 = 0

3 - 3 tan (2 x) = 4 - 23 tan (2 x)

What is the general solution for solvefor y,-1/2 cot(y)=(t^2)/(+2)+C ?
The general solution for solvefor y,-1/2 cot(y)=(t^2)/(+2)+C is y=arccot(-t^2-2C)+pin