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

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

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

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

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

Solution steps

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

Subtract

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

from both sides

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

Rewrite using trig identities

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

Solve by substitution

tan (x) = 1, tan (x) = - 1

tan (x) = 1 : x = \frac{π}{4} + πn

tan (x) = - 1 : x = \frac{3 π}{4} + πn

Combine all the solutions

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

2 tan (x) - 4 = 1

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

csc (θ) = - 2, 0 \leq θ < 4 π

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

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

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