In the triangle ABC, two sides b,c and angle B are given, side a has two values `a_(1)` and `a_(2)`. Show that `|(a_(1)-a_(2))|=2sqrt(b^(2)-c^(2)sin^(2)B)`.

In A B C , sides b , c and angle B are given such that a has two values a_1and a_2dot Then prove that |a_1-a_2|=2sqrt(b^2-c^2sin^2B)

In the triangle ABC, if the sides a,b reamain constant but the base angles A and B very, then show that, (dA)/(sqrt(a^(2) - b^(2) sin^(2)A)) = (dB)/(sqrt(b^(2) - a^(2) sin^(2)B)).

In a triangle ABC if the sides a, b be constant and the base angles A and B vary, then show that , (dA)/sqrt(a^2-b^2sin^2A) =(dB)/sqrt(b^2-a^2 sin^2B)

In a triangle ABC the angle A=60^(@) and b:c = (sqrt(3)+1):2 . Find the other two angles B and C.

If a_(1) = 2 and a_(n) - a_(n-1) = 2n (n ge 2) , find the value of a_(1) + a_(2) + a_(3)+…+a_(20) .

In any triangle ABC show that b^2sin2C+c^2sin 2B=abc/R

A triangle ABC is such that sin (2A + B) = 1/2 . If A,B,C are in A.P., then find the value of A,B and C.

In Delta ABC, a, b and A are given and c_(1), c_(2) are two values of the third side c. Prove that the sum of the area of two triangles with sides a, b, c_(1) and a, b c_(2) " is " (1)/(2) b^(2) sin 2A

In any triangle ABC if sin A sin B sin C+ cos A cos B=1 , then show that a:b:c=1:1: sqrt(2) .

Statement - I: Equation of bisectors of the angles between the liens x=0 and y=0 are y=+-x Statement - II : Equation of the bisectors of the angles between the lines a_(1)x+b_(1)y+c_(1)=0anda_(2)x+b_(2)y+c_(2)=0 are (a_(1)x+b_(1)y+c_(1))/(sqrt(a_(1)^(2)+b_(1)^(2)))=+-(a_(2)x+b_(2)y+c_(2))/(sqrt(a_(2)^(2)+b_(2)^(2))) (Provided a_(1)b_(2)nea_(2)b_(1)andc_(1),c_(2)gt0)