In `Delta ABC ` , a= 6 ,b=3 and cos (A-B) = 4/5 .Then are of triangle is

Options

A. 8 sq units
B. 9 sq units
C. 6 sq units
D. None of these

Answer

B

Explanation

`:.cos(A-B)=(4)/(5)`
`:.tan((A-B)/(2))=sqrt((1-cos(A-B))/(1+cos(A-B)))=(1)/(3)`
But `tan((A-B)/(2))=(a-b)/(a+b).cot((C)/(2))`
`:.(1)/(3)=(6-3)/(6+3).cot((C)/(2))`
`:.cot((C)/(2))\=1=cot((pi)/(4))`
`:.C=(pi)/(2)`
`:.Delta=(1)/(2)ab=(1)/(2)(6)(3)=9`