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In a triangleABC, prove that following ...

In a `triangleABC`, prove that following
(i) ` a sin (A/2+B)=(b+c) sin ""A/2` (ii) `a(cos B+cos C)=2(b+c)sin^(2)"" A/2`
(iii) `(a^(2)-c^(2))/(b^(2))=(sin (A-C))/(sin (A+C))` (iv) `(a sin (B-C))/(b^(2)-c^(2))=(b sin (C-A))/(c^(2)-a^(2))=(c sin (A-B))/(a^(2)-b^(2))`

Text Solution

Verified by Experts

The correct Answer is:
(i) `(b+c) sin""A/2` (ii) `2(b+c) sin^(2)""A/2` (iii) `(sin(A-C))/(sin (A+C))` (iv) `tan((A+B)/(2)) cot ((A-B)/(2))`
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