# (A) If in a triangle ABC, sin^2A + sin^2B = sin(A + B), then the triangle must be (i) Rightangled

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Match the following:

 Column-I Column-II (A) If in a triangle ABC, sin2A + sin2B = sin(A + B), then the triangle must be (i) Rightangled (B) If in a triangle ABC bc/(2 cos A) = b2 + c2 -  2bc cosA , then the triangle must be (ii) Equilateral (C) If in a triangle ABC,tan A/2 + tan B/2 + tan C/2 = √3, then the triangle must be (iii) Isosceles (D) If in a triangle the sides and the altitudes are in AP, then the triangle must be (iv) Obtuseangled

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Correct option  (A) → (i); (B) → (iii); (C) → (ii); (D) → (ii)

(A)  sin2 (A) + sin2 (B) = sin (A + B)

(B)  bc/2cos A = b2 + c2 - 2bc cos A

Hence, the triangle is isosceles.

The triangle is equilateral.

(D)  If a, b, c are in AP. and ha, hb, hc are in AP, where ha, hb, hc are the altitudes, then a = b = c

The triangle is equilateral