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If a^2+b^2+c^2=1 then show that value of...

If `a^2+b^2+c^2=1` then show that value of the determinant `|a^2+(b^2+c^2)costhetab a(1-costheta)c a(1-costheta)a b(1-costheta)b^2+(c^2+a^2)costhetac b(1-costheta)a c(1-costheta)b c(1-costheta)c^2+(a^2+b^2)costheta|` simplifies to `cos^2theta`

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If a^(2)+b^(2)+c^(2)=1 then |(a^(2)+(b^(2)+c^(2))costheta, ab(1-cos theta),ac(1-cos theta)),(ba(1-cos theta),b^(2)+(c^(2)+a^(2))cos theta,bc(1-cos theta)),(ca(1-cos theta),cb(1-cos theta),c^(2)+(a^(2)+b^(2))costheta)| equals

(1-costheta)/(1+costheta)=((1-costheta)/(sintheta))^2=(cosectheta-cottheta)^2

Prove that : (1-costheta)(1+costheta)(1+cot^(2)theta)=1

(sin^(2)theta)/(costheta(1+costheta))+(1+costheta)/(costheta)=?

Prove that- (1+costheta)/(1-costheta)= (cosectheta+cottheta)^2

Prove that- (1-costheta)/(1+costheta)=(cosectheta-cottheta)^2

costheta/(cosec theta+1)+costheta/(cosectheta-1)=2

(sintheta)/(1+costheta) + (1+costheta)/(sintheta) = 2 cosec theta

Prove that : (1-costheta)/(1+costheta)=(cottheta-cosectheta)^(2)

Prove that- (1-costheta)/(1+costheta)=(1/(cosectheta+cottheta))^2

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