Let a,b,c are non zero constant numbers then `lim_(r->oo)(cos(a/r)-cos(b/r)cos(c/r))/(sin(b/r)sin(c/r))` equals

Let a,b and c be the sides of a Delta ABC. If a^(2),b^(2) and c^(2) are the roots of the equation x^(3)-Px^(2)+Qx-R=0, where P,Q&R are constants,then find the value of (cos A)/(a)+(cos B)/(b)+(cos C)/(c) in terms of P,Q and R.

a , b , c are three non coplanar non zero vectors and r is any vector in space, then ( a × b )×( r × c )+( b × c )×( r × a )+( c × a )×( r × b ) is equal to) [ ⃗ [2a b ⃗ c ] ⃗ r b. 2 [ ⃗ a ⃗ b ⃗ c ] ⃗ r c. 3 [ ⃗ a ⃗ b ⃗ c ] ⃗ r d. none of these

Prove that cos A+cos B+cos C=1+(r)/(R)

Prove that cos A+cos B+cos C=1+(r)/(R)

All the notations used in statemnt I and statement II are usual. Statement I In triangle ABC, if (cos A)/(a )=(cos B)/(b)=(cos C)/(c). then value of (r_(1)+r_(2)+r_(3))/(r) is equal to 9. Statement II If Delta ABC:(a)/(sin A) =(b)/(sin B) =(c)/(sin C)=2R, where R is circumradius.

All the notations used in statemnt I and statement II are usual. Statement I: In triangle ABC, if (cos A)/(a )=(cos B)/(b)=(cos C)/(c). then value of (r_(1)+r_(2)+r_(3))/(r) is equal to 9. Statement II: In Delta ABC:(a)/(sin A) =(b)/(sin B) =(c)/(sin C)=2R, where R is circumradius.

All the notations used in statemnt I and statement II are usual. Statement I: In triangle ABC, if (cos A)/(a )=(cos B)/(b)=(cos C)/(c). then value of (r_(1)+r_(2)+r_(3))/(r) is equal to 9. Statement II: In Delta ABC:(a)/(sin A) =(b)/(sin B) =(c)/(sin C)=2R, where R is circumradius.

In triangle ABC,(cos A)/(a)=(cos B)/(b)=(cos C)/(c) The valuecos of (r_(1)+r_(2)+r_(3))/(r) is equal to