Question

- с -COS 7. For any triangle ABC, prove that s if ZB = 60

JEE/Engineering Exams

Maths

Solution

4.0 (1 ratings)

Let ( a / sin A=b / sin B=c / sin C=k ) Then, ( a=k sin A, b=k sin B, c=k sin C ) ( mathrm{RHS} ) ( mathrm{b}-mathrm{c} / mathrm{a} cos mathrm{A} / 2 ) ( =(k sin B-k sin C / k sin A) cos A / 2 ) ( ={[2 cos B+C / 2 sin B-C / 2] / sin A} cos A / 2 ) ( =left[2^{star} sin B-C / 2 cos (p i / 2-A / 2) cdot cos A / 2right] / sin A ) ( =left[sin A^{*} sin B-C / 2right] / sin A ) ( =sin B-C / 2 ) ( =mathrm{LHS} )