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

The general solution for cos(2x)+sin(x)-1=0 is x=2pin,x=pi+2pin,x= pi/6+2pin,x=(5pi)/6+2pin

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

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

x = 2 πn, x = π + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

sin (x) = 0, sin (x) = \frac{1}{2}

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

x, e^{c o s (y)} - e^{s i n (x)} = sin (y)

5 + tan (θ) = 4

arctan (e^{x}) = 0

cos (x) = 3 - cos (x)

4 sin^{2} (x) + 1 = 4 sin (x)

What is the general solution for cos(2x)+sin(x)-1=0 ?
The general solution for cos(2x)+sin(x)-1=0 is x=2pin,x=pi+2pin,x= pi/6+2pin,x=(5pi)/6+2pin