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

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

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sin(x+pi/2)+cos^2(x)=0

sin (x + \frac{π}{2}) + cos^{2} (x) = 0

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

Solution steps

sin (x + \frac{π}{2}) + cos^{2} (x) = 0

Rewrite using trig identities

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

Solve by substitution

cos (x) = 0, cos (x) = - 1

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

cos (x) = - 1 : x = π + 2 πn

Combine all the solutions

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

3 sin^{2} (x) - sin (x) - 4 = 0

sin (3 x) = sin^{2} (x)

2 cot (x) + 3 = 0

cos (x + 6 0^{\circ}) + sin (x) = 0

sin (x) \cdot cos (x) = \frac{1}{4}

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