The vertices of a triangle are `A(x_1,x_1tantheta_1),B(x_2, x_2tantheta_2),` and `C(x_3, x_3tantheta_3)dot` If the circumcenter of ` A B C` coincides with the origin and `H(a , b)` is the orthocentre, show that `a/b=(costheta_1+costheta_2+costheta_3)/(sintheta_1+sintheta_2+sintheta_3)`

The vertices of a triangle are A(x_1, x_1tantheta_1),B(x_2, x_2tantheta_2)a n dC(x_3, x_3tantheta_3)dot if the circumcentre of "Delta"A B C coincides with the origin and H( x , y ) is the orthocentre, show that y/( x )=(sintheta_1+ sintheta_2+sintheta_3)/(costheta_1+costheta_2+costheta_3)

The vertices of a triangle are A(x_1, x_1tantheta_1),B(x_2, x_2tantheta_2)a n dC(x_3, x_3tantheta_3)dot if the circumcentre of DeltaABC coincides with the origin and H( barx , bary ) is the orthocentre, show that bary/( barx )=(sintheta1+sintheta_2+sintheta_3)/(costheta_1+costheta_2+costheta_3)

The vertices of a triangle are : P(x_1,x_1 tan theta_1),Q (x_2, x_2tantheta_2) and R(x_3, x_3tantheta_3) . If the circumcentre of trianglePQR coincides with the origin and H(bar x,bar y) is the orthocentre, show that : bar y/bar x= (sintheta_1+sintheta_2+sintheta_3)/(costheta_1+costheta_2+costheta_3) .

If 3costheta-4sintheta=2costheta+sintheta , find tantheta .

If 3 cos theta-4sintheta=2costheta+sintheta find tantheta .

sintheta/(1-cottheta)+costheta/(1-tantheta)=

Prove that: (1+sintheta-costheta)/(1+sintheta+costheta)=tantheta/2

Prove that: (1+sintheta-costheta)/(1+sintheta+costheta)=tantheta/2

Prove that: (sintheta-costheta+1)/(sintheta+costheta-1)=1/(sectheta-tantheta)

Prove that (1/costheta-costheta)(1/sintheta-sintheta)=1/(tantheta+cottheta) .