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

The general solution for sin(x)=1-cos^x(x) is x=2pin

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

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

x = 2 πn

Solution steps

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

Square both sides

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

Subtract

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

from both sides

sin^{2} (x) = 0

Apply rule

x^{n} = 0 \Rightarrow x = 0

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

Verify solutions by plugging them into the original equation

x = 2 πn

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\frac{5}{tan ( x )} = - 2

tan^{22} (x) = sec^{2} (x) - 1

tan^{4} (x) + tan^{2} (x) = tan (x)

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