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

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

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sin^2(x)+cos^2(x)=sin(x)csc^2(x)

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

x = \frac{π}{2} + 2 πn

Solution steps

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

Subtract

sin (x) csc^{2} (x)

from both sides

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

Rewrite using trig identities

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

Multiply both sides by

sin (x)

- 1 + sin (x) = 0

Move

1

to the right side

sin (x) = 1

Verify Solutions

Find undefined (singularity) points:

sin (x) = 0

Combine undefined points with solutions:

sin (x) = 1

General solutions for

sin (x) = 1

x = \frac{π}{2} + 2 πn

1.5 2 = 3 cos (x)

\frac{sin ( 5 9 ^{\circ} )}{8} = \frac{sin ( x )}{9.25}

2 a \cdot cos (θ) = 0

\frac{sin ^{3} ( x )}{cos ^{3} ( x ) - cos ( x )} = tan (x)

4 sin (t) - 3 cos (t) = 0

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