The question is attached above. Please send step by step complete solution. I also request you please do not send any web link to this question because I am unable to  open the link every time  .

Asked by sudhanshubhushanroy | 14th Dec, 2017, 06:55: AM

Expert Answer:

begin mathsize 16px style straight D right parenthesis
cos left parenthesis straight A minus straight B right parenthesis equals 31 over 32
cos left parenthesis straight A minus straight B right parenthesis equals fraction numerator 1 minus tan squared open parentheses begin display style fraction numerator straight A minus straight B over denominator 2 end fraction end style close parentheses over denominator 1 plus tan squared open parentheses fraction numerator straight A minus straight B over denominator 2 end fraction close parentheses end fraction
rightwards double arrow tan open parentheses fraction numerator straight A minus straight B over denominator 2 end fraction close parentheses equals fraction numerator 1 over denominator square root of 63 end fraction
tan open parentheses fraction numerator straight A minus straight B over denominator 2 end fraction close parentheses equals fraction numerator straight a minus straight b over denominator straight a plus straight b end fraction cot straight C over 2
fraction numerator straight a minus straight b over denominator straight a plus straight b end fraction cot straight C over 2 equals fraction numerator 1 over denominator square root of 63 end fraction
rightwards double arrow tan straight C over 2 equals fraction numerator square root of 63 over denominator 9 end fraction
cosC equals fraction numerator 1 minus tan squared open parentheses begin display style straight C over 2 end style close parentheses over denominator 1 plus tan squared open parentheses straight C over 2 close parentheses end fraction equals 1 over 8
Using space straight c squared equals straight a squared plus straight b squared minus 2 abcosC
find space straight c space you space will space get space straight c equals 6.

straight C right parenthesis
Using space
Let space straight R space be space the space centre space of space circumcentre space and space straight r space be space the space incentre.
RcosA equals straight r
using space half space angle space formulae space you space get space cosB plus cosC equals 1

straight A right parenthesis
left parenthesis straight a plus straight b plus straight c right parenthesis left parenthesis straight b plus straight c minus straight a right parenthesis equals λbc
Solving space this space we space get
fraction numerator straight b squared plus straight c squared minus straight a squared over denominator 2 bc end fraction equals straight lambda over 2 minus 1
cosA equals straight lambda over 2 minus 1
minus 1 less than cosA less than 1
rightwards double arrow 0 less than straight lambda less than 4
Hence comma space straight lambda equals 3 space
end style

Answered by Sneha shidid | 18th Dec, 2017, 05:15: PM