What is the general solution for 1/4 sin(8x)=-1/8 ,2cos(8x)=sqrt(3) ?

The general solution for 1/4 sin(8x)=-1/8 ,2cos(8x)=sqrt(3) is No Solution for x\in\mathbb{R}

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1/4 sin(8x)=-1/8 ,2cos(8x)=sqrt(3)

\frac{1}{4} sin (8 x) = - \frac{1}{8}, 2 cos (8 x) = 3

No Solution for x \in R

Solution steps

\frac{1}{4} sin (8 x) = - \frac{1}{8}, 2 cos (8 x) = 3

Multiply both sides by

4

sin (8 x) = - \frac{1}{2}

General solutions for

sin (8 x) = - \frac{1}{2}

8 x = \frac{7 π}{6} + 2 πn, 8 x = \frac{11 π}{6} + 2 πn

Solve

8 x = \frac{7 π}{6} + 2 πn : x = \frac{7 π}{48} + \frac{πn}{4}

Solve

8 x = \frac{11 π}{6} + 2 πn : x = \frac{11 π}{48} + \frac{πn}{4}

x = \frac{7 π}{48} + \frac{πn}{4}, x = \frac{11 π}{48} + \frac{πn}{4}

Solutions for the range

2 cos (8 x) = 3

No Solution for x \in R

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arctan (4 x) + arctan (6 x) = 90

2 sin (θ) tan (θ) - tan (θ) = 1 - 2 sin (θ)

7 cos (2 θ) - 9 = - 9 sin (θ)

What is the general solution for 1/4 sin(8x)=-1/8 ,2cos(8x)=sqrt(3) ?
The general solution for 1/4 sin(8x)=-1/8 ,2cos(8x)=sqrt(3) is No Solution for x\in\mathbb{R}