What is the general solution for 2sin^2(x)+cos^2(x)+cos(x)-1=0 ?

The general solution for 2sin^2(x)+cos^2(x)+cos(x)-1=0 is x=2.23703…+2pin,x=-2.23703…+2pin

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

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

x = 2.23703 \dots + 2 πn, x = - 2.23703 \dots + 2 πn

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

cos (x) = - \frac{- 1 + 5}{2}, cos (x) = \frac{1 + 5}{2}

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

cos (x) = \frac{1 + 5}{2} :

No Solution

Combine all the solutions

x = arccos (- \frac{- 1 + 5}{2}) + 2 πn, x = - arccos (- \frac{- 1 + 5}{2}) + 2 πn

Show solutions in decimal form

x = 2.23703 \dots + 2 πn, x = - 2.23703 \dots + 2 πn

14 4^{2} = 43.2 7^{2} + 7 2^{2} - 2 \cdot 43.27 \cdot 72 \cdot cos (x)

sin (8 x + 48) = cos (- 4 x + 26)

3 cos (x) + sec (14 5^{\circ}) = 1

sec^{2} (x) + 3 tan^{2} (x) = 13

1609.3 = \frac{1.13 3 ^{2}}{( 9.8 ) tan ( θ )}

What is the general solution for 2sin^2(x)+cos^2(x)+cos(x)-1=0 ?
The general solution for 2sin^2(x)+cos^2(x)+cos(x)-1=0 is x=2.23703…+2pin,x=-2.23703…+2pin