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

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

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

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

x = π + 2 πn

Solution steps

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

Subtract

sin^{2} (x)

from both sides

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

Rewrite using trig identities

- 2 + d^{2} - 2 cos (x) + cos (x) d^{2} = 0

Solve by substitution

cos (x) = - 1; d \neq = 2, d \neq = - 2

cos (x) = - 1 : x = π + 2 πn

Combine all the solutions

x = π + 2 πn

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

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

\frac{sin ^{3} ( x )}{sin ( x )} = 0

sin (135 - x) = sin (x)

tan (x) - 4 = - 1

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