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

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

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

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

x = \frac{π}{4} + πn

Degrees

x = 4 5^{\circ} + 18 0^{\circ} n

Solution steps

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

Rewrite using trig identities

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

Use the Pythagorean identity:

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

= 1

1 = tan (x)

Switch sides

tan (x) = 1

General solutions for

tan (x) = 1

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = \frac{π}{4} + πn

x = \frac{π}{4} + πn

3 tan (3 x) = tan (x)

sin (x) = \frac{5}{5}, sin (2 x)

0 = 1 - cos (2 π x)

tan (θ) = \frac{12}{5}, 0 \leq θ \leq \frac{π}{2}

sin (x) = \frac{420}{2.3}

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