In a triangle ABC, (a²-b²-c²) tan A+ (a²-b²+c²) tan B is equal to

In ΔABC, r₁²+r₂²+r₃²+r² =

A man observes that angle of elevation of the top of a tower from a point P on the ground is θ. He moves a certain distance towards the foot of the tower and finds that the angle of elevation of the top has doubled. He further moves a distance 3/4 of the previous and finds that the angle of elevation is three times that at P. Then angle θ is given by

If a. cos (θ+ α)= b cos (θ-α), then (a+b) tan θ=

If α,β are solutions of a cos 2θ+b sin 2θ=c, then tan α tan β=

If sin A= sin² B and 2 cos² A =3 cos² B, then the ΔABC is

In ΔABC, if A=90⁰ then r₂ +r₃ =