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

The general solution for -cos^2(x)-sin(x)-1=0 is x=(3pi)/2+2pin

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

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

x = \frac{3 π}{2} + 2 πn

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

sin (x) = 2, sin (x) = - 1

sin (x) = 2 :

No Solution

sin (x) = - 1 : x = \frac{3 π}{2} + 2 πn

Combine all the solutions

x = \frac{3 π}{2} + 2 πn

- 8 cos^{2} (x) + 1 = 4 sin^{2} (x) - 8 cos (x)

\frac{1 + csc ( y )}{cot ( y ) + cos ( y )} = csc (y)

2 = sin (10 x)

cos (2 x) = \frac{( 2 k - 8 )}{9}

x, h = tan (x - \frac{π}{4})

What is the general solution for -cos^2(x)-sin(x)-1=0 ?
The general solution for -cos^2(x)-sin(x)-1=0 is x=(3pi)/2+2pin