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In a Delta ABC, 2 sinA cos B + 2 sin B c...

In a `Delta ABC`, 2 sinA cos B + 2 sin B cos C + 2 sin cos A = sin A + sin B + sin C, then `Delta ABC`is

A

isosceles

B

right angled

C

acute angled

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Given
`sin(A+B)+sin(A-B)+sin (B+C)+sin(B-C)+sin (C+A)+sin(C-A)`
`= sin A + sin B + sin C`
`rArr sin(A-B)+sin (B-C)+sin(C-A)=0`
`rArr 4 sin.(A-B)/(2)sin.(B-C)/(2)sin.(C-A)/(2)=0`
`therefore Delta` is isosceles.
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