नेपियर की समानता `"tan"(B-C)/(2)=(b-c)/(b+c)"cot"(A)/(2)` सिद्ध कीजिए |

Explanation

चूँकि `" " (b-c)/(b+c)=(k sin B-k sin C)/(k sin B + k sin C)=(sin B - sin C)/(sin B + sin C)`
`=("2 sin"(B-C)/(2)"cos"(B+C)/(2))/("2 cos"(B-C)/(2)"sin"(B+C)/(2))`
`=(("sin"(B-C)/(2))/("cos"(B-C)/(2))).(("cos"(B+C)/(2))/("sin"(B+C)/(2)))`
`rArr " " (b-c)/(b+c)="tan"(B-C)/(2)"cot"(B+C)/(2)`
`="tan"(B-C)/(2)cot((pi)/(2)-(A)/(2))`
`= "tan"(B-C)/(2)"tan"(A)/(2)`
`rArr " tan"(B-C)/(2)=(b-c)/(b+c)"cot"(A)/(2)`
`rArr " " L.H.S. = R.H.S. " "` इति सिद्धम्