What is the general solution for 1+2cos(x)+cos^2(x)=3sin^2(x) ?

The general solution for 1+2cos(x)+cos^2(x)=3sin^2(x) is x= pi/3+2pin,x=(5pi)/3+2pin,x=pi+2pin

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1+2cos(x)+cos^2(x)=3sin^2(x)

1 + 2 cos (x) + cos^{2} (x) = 3 sin^{2} (x)

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn, x = π + 2 πn

Solution steps

1 + 2 cos (x) + cos^{2} (x) = 3 sin^{2} (x)

Subtract

3 sin^{2} (x)

from both sides

1 + 2 cos (x) + cos^{2} (x) - 3 sin^{2} (x) = 0

Rewrite using trig identities

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

Solve by substitution

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

cos (x) = \frac{1}{2} : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

cos (x) = - 1 : x = π + 2 πn

Combine all the solutions

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn, x = π + 2 πn

L, sin (k L) = 0

cos (- x) = 2, sec (x) + cos (x)

2 \cdot sin (3 θ) = 2

cos (x) = \frac{9.8}{( 0.1 ) ( 6.28 ) ^{2}}

cos^{4} (x) - 3 cos^{2} (x) - 4 = 0

What is the general solution for 1+2cos(x)+cos^2(x)=3sin^2(x) ?
The general solution for 1+2cos(x)+cos^2(x)=3sin^2(x) is x= pi/3+2pin,x=(5pi)/3+2pin,x=pi+2pin