What is the general solution for 2/(tan(a)+cot(a))=2sin(a) ?

The general solution for 2/(tan(a)+cot(a))=2sin(a) is No Solution for a\in\mathbb{R}

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2/(tan(a)+cot(a))=2sin(a)

\frac{2}{tan ( a ) + cot ( a )} = 2 sin (a)

No Solution for a \in R

Solution steps

\frac{2}{tan ( a ) + cot ( a )} = 2 sin (a)

Subtract

2 sin (a)

from both sides

\frac{2}{tan ( a ) + cot ( a )} - 2 sin (a) = 0

Simplify

\frac{2}{tan ( a ) + cot ( a )} - 2 sin (a) : \frac{2 - 2 sin ( a ) ( tan ( a ) + cot ( a ) )}{tan ( a ) + cot ( a )}

\frac{2 - 2 sin ( a ) ( tan ( a ) + cot ( a ) )}{tan ( a ) + cot ( a )} = 0

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

2 - 2 sin (a) (tan (a) + cot (a)) = 0

Express with sin, cos

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

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

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

Rewrite using trig identities

2 cos (a) - 2 \cdot 1 = 0

Multiply the numbers:

2 \cdot 1 = 2

2 cos (a) - 2 = 0

Move

2

to the right side

2 cos (a) = 2

Divide both sides by

2

cos (a) = 1

General solutions for

cos (a) = 1

a = 0 + 2 πn

Solve

a = 0 + 2 πn : a = 2 πn

a = 2 πn

Since the equation is undefined for:

2 πn

No Solution for a \in R

2 sin^{2} (w) + 3 sin (w) + 1 = 0

tan (x) - 2 tan (x) cos (x) = 0

sin (t) cos (t) = cos (t)

- 7 cos (7 x) = 0

1 - 4 sin^{2} (x) = 0

What is the general solution for 2/(tan(a)+cot(a))=2sin(a) ?
The general solution for 2/(tan(a)+cot(a))=2sin(a) is No Solution for a\in\mathbb{R}