If cos^2θ+sinθ+1=0 then find the principal solution.

Steps to solve cos^2θ+sinθ+1=0 then find the principal solution.

⇒cos^2θ+sinθ+1=0

⇒1-sin^2θ+sinθ+1=0

⇒sin^2θ-sinθ-2=0

⇒sin^2θ-2sinθ+sinθ-2=0

⇒sinθ(sinθ-2)+1(sinθ-2)=0

⇒(sinθ-2)(sinθ+1)=0

⇒sinθ=2 and sinθ=-1

sinθ=-1

⇒sinθ=sin(-π/2)

⇒θ=nπ+(-1)^n(π/2)

n=0
⇒θ=0π+(-1)^0(π/2)=-π/2

n=1
⇒θ=1π+(-1)^1(π/2)=π/2

n=2
⇒θ=2π+(-1)^2(π/2)=5π/2

Hence the principal solution of cos^2θ+sinθ+1=0 is π/2

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