What is the general solution for tan(a)= 5/12 ,sin(a)<0,sin(a)+cos(a) ?

The general solution for tan(a)= 5/12 ,sin(a)<0,sin(a)+cos(a) is No Solution for a\in\mathbb{R}

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tan(a)= 5/12 ,sin(a)<0,sin(a)+cos(a)

tan (a) = \frac{5}{12}, sin (a) < 0, sin (a) + cos (a)

No Solution for a \in R

Solution steps

tan (a) = \frac{5}{12}, sin (a) < 0, sin (a) + cos (a)

Apply trig inverse properties

a = arctan (\frac{5}{12}) + πn

Solutions for the range

sin (a) < 0

No Solution for a \in R

cot (2 x) = 3, 0 \leq x \leq 2 π

cot (θ) = \frac{5}{3}

cos (2 θ) = \frac{3}{5}

cos (\frac{x}{3}) = \frac{1}{2}

3 cos (2 x) - 5 cos (x) = 1

What is the general solution for tan(a)= 5/12 ,sin(a)<0,sin(a)+cos(a) ?
The general solution for tan(a)= 5/12 ,sin(a)<0,sin(a)+cos(a) is No Solution for a\in\mathbb{R}