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

The general solution for sin^2(x/2)+cos(x)=0 is x=pi+4pin,x=3pi+4pin

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

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

x = π + 4 πn, x = 3 π + 4 πn

Solution steps

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

Rewrite using trig identities

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

Apply rule

x^{n} = 0 \Rightarrow x = 0

cos (\frac{x}{2}) = 0

General solutions for

cos (\frac{x}{2}) = 0

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

Solve

\frac{x}{2} = \frac{π}{2} + 2 πn : x = π + 4 πn

Solve

\frac{x}{2} = \frac{3 π}{2} + 2 πn : x = 3 π + 4 πn

x = π + 4 πn, x = 3 π + 4 πn

3 cos (x) + 1 = 1

sin (θ - \frac{π}{3}) + 1 = 0

tan^{2} (2 θ) = tan (2 θ)

2 cos (2 x) = 2 sin (x)

- sin (θ) + 1 + cos (θ) = 0

What is the general solution for sin^2(x/2)+cos(x)=0 ?
The general solution for sin^2(x/2)+cos(x)=0 is x=pi+4pin,x=3pi+4pin