What is the general solution for (cos^{2022}(x))/((sin^{2022)(x)+cos^{2022}(x))}=1 ?

The general solution for (cos^{2022}(x))/((sin^{2022)(x)+cos^{2022}(x))}=1 is x=2pin,x=pi+2pin

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(cos^{2022}(x))/((sin^{2022)(x)+cos^{2022}(x))}=1

\frac{cos ^{2022} ( x )}{( sin ^{2022} ( x ) + cos ^{2022} ( x ) )} = 1

x = 2 πn, x = π + 2 πn

Solution steps

\frac{cos ^{2022} ( x )}{( sin ^{2022} ( x ) + cos ^{2022} ( x ) )} = 1

Subtract

1

from both sides

\frac{cos ^{2022} ( x )}{sin ^{2022} ( x ) + cos ^{2022} ( x )} - 1 = 0

Simplify

\frac{cos ^{2022} ( x )}{sin ^{2022} ( x ) + cos ^{2022} ( x )} - 1 : - \frac{sin ^{2022} ( x )}{sin ^{2022} ( x ) + cos ^{2022} ( x )}

- \frac{sin ^{2022} ( x )}{sin ^{2022} ( x ) + cos ^{2022} ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

- (sin^{2022} (x)) = 0

Divide both sides by

- 1

sin^{2022} (x) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

sin (x) = 0

The solution is

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

5 sec (x) - 4 cos (x) = 8

sin^{3} (x) = - 1

x, sin^{2} (x) = \frac{( 1 - cos ( y ) )}{2}

sin (x) + sin^{2} (x) + cos (x) + cos^{2} (x) = 0

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

What is the general solution for (cos^{2022}(x))/((sin^{2022)(x)+cos^{2022}(x))}=1 ?
The general solution for (cos^{2022}(x))/((sin^{2022)(x)+cos^{2022}(x))}=1 is x=2pin,x=pi+2pin