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)`

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))

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 in triangle ABC, a, c and angle A are given and c sin A lt a lt c , then ( b_(1) and b_(2) are values of b)

In A B C , prove that (a-b^2cos^2C/2+(a+b)^2sin^2C/2=c^2dot

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

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)

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 vec a=a_1 hat i+a_2 hat j+a_3 hat k , vec b=b_1 hat i+b_2 hat j+b_3 hat ka n d vec c=c_1 hat i+c_2 hat j+c_3 hat k be three non-zero vectors such that vec c is a unit vector perpendicular to both vec aa n d vec b . If the angle between aa n db is pi/6, then prove that |(a_1 a_2a_3)(b_1b_2b_3)(c_1c_2c_3)|=1/4(a1 2+a2 2+a3 2)(b1 2+b2 2+b3 2)

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))

In a scalene triangle A B C ,D is a point on the side A B such that C D^2=A D D B , sin s in A S in B=sin^2C/2 then prove that CD is internal bisector of /_Cdot