Find (i) `sin C (ii) cos C and (iii) tan C ` in the adjacent triangle.

In a triangle ABC, if (cos A)/(a) =(cos B)/(b ) =(cos C)/(c) and the side a=2, then the area of the triangle is-

If in a triangle ABC, b sin B = c sin C, then the triangle is-

(i) If in a triangle ABC, a^(4) + b^(4) +c^(4) - 2b^(2) c^(2) -2c^(2)a^(2)=0 , then show that, C=45^(@) or 135^(@) . (ii) In in a triangle ABC, sin^(4)A + sin^(4)B + sin^(4)C = sin^(2)B sin^(2)C + 2sin^(2) C sin^(2)A + 2sin^(2)A sin^(2)B , show that, one of the angles of the triangle is 30^(@) or 150^(@)

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)=asin((B-C)/2) (c) (b+c)sin((B+C)/2)=acosA/2 (d) (b-c)cos(A/2)=2asin(B+C)/2

The corodinates of the three vertices of a triangle are (a, a tan alpha) , (b ,b tan beta) and (c, c tangamma) . If the circumcentre and orthocentre of the triangle are at (0,0) and (h,k) respectively, prove that (h)/(k)=(cos alpha+ cos beta+ cos gamma)/( sin alpha+ sin beta + sin gamma) .

In any triangle ABC, if (cos A + 2 cos C)/(cos A + 2 cos B) = (sin B)/(sin C) then prove that, the triangle is either isosceles or right angled.

If in a triangle ABC ,(sin A+sin B +sin C)(sinA+sinB-sin C)=3sinAsinB then angle C is equal to

(i) If a:b:c= 2:3:4 and s=27 inches, find the area of the triangle ABC. (ii) If in a triangle ABC, a=6, b=3 and cos(A-B) =4/5 then find its area.

Find the minimum values of: "sin" ^(2) (A)/(2)+"sin"^(2)(B)/(2) +"sin" (C)/(2) where A,B,C are the angles of a triangle.