The three sides of a triangle are `L_(r) + x cos theta_(r) + y sin theta _(r) - p_(r) = 0 ` where r = 1,2,3 . Show that the orthocentre is given by
`L_(1) cos (theta_(2)-theta_(3)) = L_(2)cos (theta_(3)-theta_(1)) = L_(3)cos (theta_(1)-theta_(2))` .

If sintheta_(1)+sintheta_(2)+sintheta_(3)=3, then cos theta_(1)+cos theta_(2)+cos theta_(3)=

If sintheta_(1)+sintheta_(2)+sintheta_(3)=3 , then cos theta_(1)+cos theta_(2)+cos theta_(3)=

Prove : (cos theta)/(1+sin theta) + (cos theta)/(1-sin theta)= 2 sec theta

Vertices of a variable triangle are (3, 4), (5 cos theta, 5 sin theta) and (5 sin theta, -5 cos theta) , where theta in R . Locus of its orthocentre is

Prove that (cos^3 theta-sin^3 theta)/(cos theta-sin theta) = 1+cos theta sin theta

Let z_(1),z_(2) and z_(3) be three points on |z|=1 . If theta_(1), theta_(2) and theta_(3) be the arguments of z_(1),z_(2),z_(3) respectively, then cos(theta_(1)-theta_(2))+cos(theta_(2)-theta_(3))+cos(theta_(3)-theta_(1))

cos2 theta*cos(theta/(2))-cos3 theta*cos((9theta)/2)=sin5 theta*sin((5theta)/(2))

Prove that : (2 cos^(3) theta-cos theta)/(sin theta-2 sin^(3)theta)=cot theta

(1+sin 2theta+cos 2theta)/(1+sin2 theta-cos 2 theta) =

If (cos theta_(1))/(cos theta_(2))+(sin theta_(1))/(sin theta_(2))=(cos theta_(0))/(cos theta_(2))+(sin theta_(0))/(sin theta_(2))=1 , where theta_(1) and theta_(0) do not differ by can even multiple of pi , prove that (cos theta_(1)*cos theta_(0))/(cos^( 2)theta_(2))+(sin theta_(1)*sin theta_(0))/(sin^(2) theta_(2))=-1