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

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

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

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

x = \frac{π}{2} + πn

Solution steps

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

Subtract

1

from both sides

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

Simplify

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

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

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

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

Rewrite using trig identities

1 + cos (2 x) = 0

Move

1

to the right side

cos (2 x) = - 1

General solutions for

cos (2 x) = - 1

2 x = π + 2 πn

Solve

2 x = π + 2 πn : x = \frac{π}{2} + πn

x = \frac{π}{2} + πn

\frac{sin ^{2} ( θ ) - 2 sin ( θ ) + 1}{sin ( θ ) - 1} = - 1

w, 100 cos (10 w) = 50

cos (θ) = \frac{8}{25}

sin (2 x) = π

sin (x + 5 π) = 0

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