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

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

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cos(x)=sin^2(x)

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

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

Solution steps

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

Subtract

sin^{2} (x)

from both sides

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

cos (b) = \frac{11}{14}

sin (x) - cos (x) = - 1, 0 \leq x \leq 2 π

cos (θ) = (\frac{1}{2})

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

cos (θ) = - cos (2 θ)

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