In ` A B C ,a , ca n dA` are given and `b_1,b_2` are two values of the third side `b` such that `b_2=2b_1dot` Then prove that `sinA=sqrt((9a^2-c^2)/(8c^2))`

In A B C ,s i d e sb , c and angle B are given such that a has two valus a_1a n da_2dot Then prove that |a_1-a_2|=2sqrt(b^2-c^2sin^2B)

If C is the center and A ,B are two points on the conic 4x^2+9y^2-8x-36 y+4=0 such that /_A C B=pi/2, then prove that 1/(C A^2)+1/(C B^2)=(13)/(36)dot

If the sides a , b and c of A B C are in AdotPdot, prove that 2sin(A/2)sin(C/2)=sin(B/2)

In triangle A B C ,a , b , c are the lengths of its sides and A , B ,C are the angles of triangle A B Cdot The correct relation is given by (a) (b-c)sin((B-C)/2)=acosA/2 (b) (b-c)cos(A/2)=as in(B-C)/2 (c) (b+c)sin((B+C)/2)=acosA/2 (d) (b-c)cos(A/2)=2asin(B+C)/2

If a ,b ,a n dc are in G.P. then prove that 1/(a^2-b^2)+1/(b^2)=1/(b^2-c^2)dot

If the sides a , b and c of ABC are in AP dotPdot, prove that 2sinA/2sinC/2=sinB/2 acos^2C/2+cos^2A/2=(3b)/2

If cos (A /2) =sqrt((b+c)/(2c)) , then prove that a^2+b^2=c^2dot

If the segments joining the points A(a , b)a n d\ B(c , d) subtends an angle theta at the origin, prove that : costheta=(a c+b d)/sqrt((a^2+b^2)(c^2+d^2))

If area of A B C() and angle C are given and if the side c opposite to given angle is minimum, then a=sqrt((2)/(sinC)) (b) b=sqrt((2)/(sinC)) a=sqrt((4)/(sinC)) (d) b=sqrt((4)/(sinC))

Let A B C be a given isosceles triangle with A B=A C . Sides A Ba n dA C are extended up to Ea n dF , respectively, such that B ExC F=A B^2dot Prove that the line E F always passes through a fixed point.