What is the general solution for 4cot^2(x)=cos^2(x)+sin^2(x)-1 ?

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

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4cot^2(x)=cos^2(x)+sin^2(x)-1

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

x = \frac{π}{2} + πn

Solution steps

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

Subtract

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

from both sides

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

Rewrite using trig identities

1 + 4 cot^{2} (x) - 1 = 0

Move

1

to the right side

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

Move

1

to the right side

4 cot^{2} (x) = 0

Divide both sides by

4

cot (x) = 0

General solutions for

cot (x) = 0

x = \frac{π}{2} + πn

sin (3 x) cos (x) - cos (3 x) sin (x) = 0

4 sin (2 x) = - 2

x, sin^{2} (x) = 0

cos (t) = - \frac{3}{4}

sin (2 x) - 2 cos (x) = 2 sin (x) - 1

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