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

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

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

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

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Solution steps

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

Subtract

sin^{2} (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

cos (x) = 0, cos (x) = - 2

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

cos (x) = - 2 :

No Solution

Combine all the solutions

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

4 cos^{2} (x) - 11 cos (x) + 7 = 0

3 tan (x) + 2 sec (x) = 1

cos (a) = 0.14

\frac{1 + cos ^{2} ( x )}{sin ^{2} ( x )} = \frac{1}{sin ^{2} ( x )}

7 sin (a) = \frac{1}{11}

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