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Question: In a DABC, if ![](https://cdn.pureessence.tech/canvas_478.png?top_left_x=900&top_left_y=1011&width=3...

In a DABC, if = 0 then sin2 A + sin2 B + sin2 C is

equal to –

A

94\frac { 9 } { 4 }

B

49\frac { 4 } { 9 }

C

1

D

33\sqrt { 3 }

Answer

94\frac { 9 } { 4 }

Explanation

Solution

= 0

Ž a2 + b2 + c2 – ab – bc – ca = 0

Ž (a – b)2 + (b – c)2 + (c – a)2 = 0

i.e. a = b = c i.e. A = B = C = 600

or sin A = sin B = sin C = 32\frac { \sqrt { 3 } } { 2 }

\sin2A + sin2B + sin2C = 94\frac { 9 } { 4 }