If `a^2+b^2+c^2=1,` then `|(a^2+(b^2+c^2)cosphi, ab(1-cosphi), ac(1-cosphi)), (ba(1-cosphi), b^2+(c^2+a^2)cosphi, bc(1-cosphi)), (ca(1-cosphi), cb(1-cosphi), c^2+(a^2+b^2)cosphi)|` is independent of

If a^(2)+b^(2)+c^(2)=1, then prove that a^(2)+(b^(2)+c^(2))cos phi,ab(1-cos phi),ac(1-cos phi)ba(1-cos phi),b^(2)+(c^(2)+a^(2))cos phi,bc(1-cos phi)ca(1-cos phi),cb(1-cos phi),c^(2)+(a^(2)+b^(2))cos phi is independent of a,b,c.

If a^2+b^2+c^2=1, then prove that |[a^2 +(b^2+c^2)cosθ, ab(1−cosθ), ac(1−cosθ)],[ba(1−cosθ),b^2(c^2+a^2)cosθ,bc(1−cosθ)],[ca(1−cosθ),cb(1−cosθ),c^2+(a^2+b^2)cosθ]| independent of a,b,c?

If a^2+b^2+c^2=1, then prove that |[a^2 +(b^2+c^2)cosθ, ab(1−cosθ), ac(1−cosθ)],[ba(1−cosθ),b^2+(c^2+a^2)cosθ,bc(1−cosθ)],[ca(1−cosθ),cb(1−cosθ),c^2+(a^2+b^2)cosθ]| independent of a,b,c?

If a^2+b^2+c^2=1, |[a^2 +(b^2+c^2)cosθ, ab(1−cosθ), ac(1−cosθ)],[ba(1−cosθ),b^2(c^2+a^2)cosθ,bc(1−cosθ)],[ca(1−cosθ),cb(1−cosθ),c^2+(a^2+b^2)cosθ]| then prove that the value of determinant is independent of a,b,c?

Show that ((1+cosphi+isinphi)/(1+cosphi-isinphi))^n=cosnphi+i sin nphi

Show that ((1+cosphi+isinphi)/(1+cosphi-isinphi))^n=cosphinphi+i sin nphi

Find int((3sinphi-2)cosphi)/(5-cos^(2)phi-4sinphi)dphi

Find int((3sinphi-2)cosphi)/(5-cos^(2)phi-4sinphi)dphi