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

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

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

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

x = 2 πn, x = π + 2 πn

Solution steps

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

Rewrite using trig identities

sin (x) + 1 = 1

Subtract

1

from both sides

sin (x) + 1 - 1 = 1 - 1

Simplify

sin (x) = 0

General solutions for

sin (x) = 0

x = 0 + 2 πn, x = π + 2 πn

Solve

x = 0 + 2 πn : x = 2 πn

x = 2 πn, x = π + 2 πn

tan (3 x) = 5 tan (x)

2 cos (2 x) - 2 = 0

3 tan^{2} (x) + 4 sec (x) = - 4

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

18 cos (10 x) + 2 = 10

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