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)

Subtract

6 (cos (x) + 1)

from both sides

sin^{2} (x) - 6 (cos (x) + 1) = 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 cos^{2} (x) - cos (x) = 1, 0 \leq x \leq 2 π

7 sin^{2} (θ) - 36 sin (θ) + 5 = 0

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

tan (\frac{2 x}{3}) = 0

3 cos^{2} (A) + 3 cos (A) = 0

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