Let `A B C` be a triangle with incentre at `I` Also, let `P` and `Q` be the feet of perpendiculars from `A` to `BI` and `CI` respectively. Then which of the following results are correct? `(A P)/(B I)=(sinB/2cosC/2)/(sinA/2)` (b) `(A Q)/(C I)=(sinC/2cosB/2)/(sinA/2)` `(A P)/(B I)=(sinC/2cosB/2)/(sinA/2)` (d) `(A P)/(B I)+(A Q)/(C I)=sqrt(3)if/_A=60^0`

Let ABC be a triangle with incentre I. If P and Q are the feet of the perpendiculars from A to BI and CI, respectively, then prove that (AP)/(BI) + (AQ)/(Cl) = cot.(A)/(2)

Let A and B be square matrices of the same order such that A^(2)=I and B^(2)=I , then which of the following is CORRECT ?

ABC is a right triangle right angled at C. Let BC = a, CA = b, AB = c and let p be the length of perpendicular from C on AB. Prove that (i) pc = ab (ii) (1)/(p^(2)) = (1)/(a^(2)) + (1)/(b^(2)) .

Show that (1+sinA)/(cosA)+(cosB)/(1-sinB)=(2sinA-2sinB)/(sin(A-B)+cosA-cosB)

Let PQR be a triangle of area Delta with a=2,b=7/2 and c=5/2 , where a,b and c are the lengths of the sides of the triangle opposite to the angles at P,Q and R respectively. Then ((2sinP-sin2P)/ (2sinP+sin2P)) equals

Let A B C be a triangle with incenter I and inradius rdot Let D ,E ,a n dF be the feet of the perpendiculars from I to the sides B C ,C A ,a n dA B , respectively. If r_1,r_2a n dr_3 are the radii of circles inscribed in the quadrilaterals A F I E ,B D I F ,a n dC E I D , respectively, prove that (r_1)/(r-1_1)+(r_2)/(r-r_2)+(r_3)/(r-r_3)=(r_1r_2r_3)/((r-r_1)(r-r_2)(r-r_3))

In A B C , the three bisectors of the angle A, B and C are extended to intersect the circumcircle at D,E and F respectively. Prove that A DcosA/2+B EcosB/2+C FcosC/2=2R(sinA+sinB+sinC)

Prove that (sinA+sinB)/(sinA-sinB)=tan((A+B)/2)cot((A-B)/2)

Let's find the L.C.M of the following algebraic expressions. p^2- q^2, (p+q)^2

Let's find the L.C.M of the following algebraic expressions. p^2 - q^2 , (p-q)^2