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

The general solution for cos(x)-sin^2(x)=0 is x=0.90455…+2pin,x=2pi-0.90455…+2pin

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

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

x = 0.90455 \dots + 2 πn, x = 2 π - 0.90455 \dots + 2 πn

Solution steps

cos (x) - sin^{2} (x) = 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 = 2 π - 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 = 2 π - arccos (\frac{- 1 + 5}{2}) + 2 πn

Show solutions in decimal form

x = 0.90455 \dots + 2 πn, x = 2 π - 0.90455 \dots + 2 πn

4 sin^{2} (x) + 9 = 12

tan (- 60 s) = - tan (6 0^{\circ})

3 cos^{2} (x) - 5 cos (x) - 2 = 0, (0^{\circ}, 36 0^{\circ})

3 - 5 cos (x) = 0

9 cos (2 θ) = 0

What is the general solution for cos(x)-sin^2(x)=0 ?
The general solution for cos(x)-sin^2(x)=0 is x=0.90455…+2pin,x=2pi-0.90455…+2pin