Match each condition to the triangle classification. List I List II (A) s i n 2 A+ s i n 2 B=sin(A+B). (P) right angled (B) bc/(2cos A)= b 2 + c 2 -2bc cos A. (Q) equilateral (C) tan(A/2)+tan(B/2)+tan

Question

Match each condition to the triangle classification. List I List II (A) s i n 2 A+ s i n 2 B=sin(A+B). (P) right angled (B) bc/(2cos A)= b 2 + c 2 -2bc cos A. (Q) equilateral (C) tan(A/2)+tan(B/2)+tan(C/2)= 3 ​ . (R) isosceles (D) Corresponding sides and altitudes are both in arithmetic progression. (S) obtuse angled

TestHub · Accepted Answer

A simplifies to cos C=0. In B, cosine rule factors the condition as ( a 2 - b 2 )( a 2 - c 2 )=0. The half-angle tangent sum attains 3 ​ at equilateral shape in C. Altitudes are inversely proportional to sides, so simultaneous arithmetic progressions in D force equal sides.

Mathematics - Properties of Triangle Question with Solution | TestHub

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Doubts & Discussion

List I	List II
(A) $s i n^{2}$ A+ $s i n^{2}$ B=sin(A+B).	(P) right angled
(B) bc/(2cos A)= $b^{2}$ + $c^{2}$ -2bc cos A.	(Q) equilateral
(C) tan(A/2)+tan(B/2)+tan(C/2)= $3$ .	(R) isosceles
(D) Corresponding sides and altitudes are both in arithmetic progression.	(S) obtuse angled