What is the general solution for sin^2(x)=6(cos(-x)+1) ?

The general solution for sin^2(x)=6(cos(-x)+1) is x=pi+2pin

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sin^2(x)=6(cos(-x)+1)

sin^{2} (x) = 6 (cos (- x) + 1)

x = π + 2 πn

Solution steps

sin^{2} (x) = 6 (cos (- x) + 1)

Rewrite using trig identities

sin^{2} (x) = 6 (1 + cos (x))

Subtract

6 (1 + cos (x))

from both sides

sin^{2} (x) - 6 (1 + cos (x)) = 0

Rewrite using trig identities

- 5 - cos^{2} (x) - 6 cos (x) = 0

Solve by substitution

cos (x) = - 5, cos (x) = - 1

cos (x) = - 5 :

No Solution

cos (x) = - 1 : x = π + 2 πn

Combine all the solutions

x = π + 2 πn

2 sin (θ) = 3 cos (θ)

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

sin (θ) = - \frac{7}{25}, cos (\frac{θ}{2}), 27 0^{\circ} < θ < 36 0^{\circ}

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

x, cos (2 x) = sin (x)

What is the general solution for sin^2(x)=6(cos(-x)+1) ?
The general solution for sin^2(x)=6(cos(-x)+1) is x=pi+2pin