What is the general solution for (tan^2(x)-4)/(cos(x)+5)=0 ?

The general solution for (tan^2(x)-4)/(cos(x)+5)=0 is x=1.10714…+pin,x=-1.10714…+pin

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(tan^2(x)-4)/(cos(x)+5)=0

\frac{tan ^{2} ( x ) - 4}{cos ( x ) + 5} = 0

x = 1.10714 \dots + πn, x = - 1.10714 \dots + πn

Solution steps

\frac{tan ^{2} ( x ) - 4}{cos ( x ) + 5} = 0

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

tan^{2} (x) - 4 = 0

Solve by substitution

tan (x) = 2, tan (x) = - 2

tan (x) = 2 : x = arctan (2) + πn

tan (x) = - 2 : x = arctan (- 2) + πn

Combine all the solutions

x = arctan (2) + πn, x = arctan (- 2) + πn

Show solutions in decimal form

x = 1.10714 \dots + πn, x = - 1.10714 \dots + πn

cot^{2} (x) = sec^{2} (x) - 1

\frac{cos ^{2} ( a ) - 1}{sin ^{2} ( a ) + 1} = 0

7 sin^{2} (x) + 2 sin^{2} (x) - 3 cos^{2} (x) = 0

sin^{2} (x) - cos^{2} (x) = cos^{4} (x)

sin^{2} (x) + 2 cos^{2} (x) = 1

What is the general solution for (tan^2(x)-4)/(cos(x)+5)=0 ?
The general solution for (tan^2(x)-4)/(cos(x)+5)=0 is x=1.10714…+pin,x=-1.10714…+pin