What is the general solution for (tan(x^2+6)-1)/(tan(x))=0 ?

The general solution for (tan(x^2+6)-1)/(tan(x))=0 is No Solution for x\in\mathbb{R}

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(tan(x^2+6)-1)/(tan(x))=0

\frac{tan ( x ^{2} + 6 ) - 1}{tan ( x )} = 0

No Solution for x \in R

Solution steps

\frac{tan ( x ^{2} + 6 ) - 1}{tan ( x )} = 0

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

tan (x^{2} + 6) - 1 = 0

Move

1

to the right side

tan (x^{2} + 6) = 1

General solutions for

tan (x^{2} + 6) = 1

x^{2} + 6 = \frac{π}{4} + πn

Solve

x^{2} + 6 = \frac{π}{4} + πn : x = \frac{π + 4 πn - 24}{2}, x = - \frac{π + 4 πn - 24}{2}

x = \frac{π + 4 πn - 24}{2}, x = - \frac{π + 4 πn - 24}{2}

Since the equation is undefined for:

\frac{π + 4 πn - 24}{2}, - \frac{π + 4 πn - 24}{2}

No Solution for x \in R

tan (θ) = \frac{8}{- 8}

4 cos^{2} (x) + 4 sin (x) = 5

sin (θ) cot (θ) = \frac{3}{2}

cos^{2} (θ) + \frac{1 0 ^{2}}{9.81 ( 1 )} cos (θ) - 1 = 0

cos^{4} (x) = \frac{1}{16}

What is the general solution for (tan(x^2+6)-1)/(tan(x))=0 ?
The general solution for (tan(x^2+6)-1)/(tan(x))=0 is No Solution for x\in\mathbb{R}