What is the general solution for (cos^2(x))/(sin^2(x))=1 ?

The general solution for (cos^2(x))/(sin^2(x))=1 is x= pi/4+pin,x=(3pi)/4+pin

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(cos^2(x))/(sin^2(x))=1

\frac{cos ^{2} ( x )}{sin ^{2} ( x )} = 1

x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn

Solution steps

\frac{cos ^{2} ( x )}{sin ^{2} ( x )} = 1

Subtract

1

from both sides

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

Simplify

\frac{cos ^{2} ( x )}{sin ^{2} ( x )} - 1 : \frac{cos ^{2} ( x ) - sin ^{2} ( x )}{sin ^{2} ( x )}

\frac{cos ^{2} ( x ) - sin ^{2} ( x )}{sin ^{2} ( x )} = 0

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

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

Rewrite using trig identities

cos (2 x) = 0

General solutions for

cos (2 x) = 0

2 x = \frac{π}{2} + 2 πn, 2 x = \frac{3 π}{2} + 2 πn

Solve

2 x = \frac{π}{2} + 2 πn : x = \frac{π}{4} + πn

Solve

2 x = \frac{3 π}{2} + 2 πn : x = \frac{3 π}{4} + πn

x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn

x, f = \frac{cos ( 2 x )}{cos ( x ) - sin ( x )}

cos (2 x) + 5 = 6.25

sin (x) = 4 sin (8)

800 cos (x) + 800 cos^{2} (x) - 800 sin^{2} (x) = 0

csc (x) = \frac{7}{3}

What is the general solution for (cos^2(x))/(sin^2(x))=1 ?
The general solution for (cos^2(x))/(sin^2(x))=1 is x= pi/4+pin,x=(3pi)/4+pin