Home
Class 12
MATHS
In any triangle ABC, prove that tan((A-...

In any `triangle ABC`, prove that tan`((A-B)/(2))=((a-b)/(a+b))cot (C)/(2)`.

Text Solution

Verified by Experts

By sine rule ,
`(a)/(sinA)=(b)/(sinB)=(c)/(sinC)=k`
` therefore a= k sin A,b = k sin B , c = k sin C`
RHS `=((a-b)/(a+b))cot.(C)/(2)` .
`= ((ksinA-ksinB)/(k sin A + k sin B))cot. (C)/(2)`
`= ((sinA-sinB)/( sin A + sin B))cot. (C)/(2)`
`=(2cos.((A+B)/(2)).sin((A-B)/(2)))/(2sin.((A+B)/(2)).cos.((A-B)/(2)))xx(cos.(C)/(2))/(sin.(C)/(2))`
`=(cos.((pi)/(2)-(C)/(2)).sin.((A-B)/(2)))/(sin.((pi)/(2)-(C)/(2)).cos.((A-B)/(2)))xx(cos.(C)/(2))/(sin.(C)/(2))" ".......[because A+B+C=pi]`
`=(sin.(C)/(2))/(cos.(C)/(2))xxtan((A-B)/(2))xx(cos.(C)/(2))/(sin.(C)/(2))`
`=tan((A-B)/(2))=`LHS.
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise Theory Questions|1 Videos

  • TRIGONOMETRIC FUNCTIONS

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise Examples for Practise|44 Videos

  • THREE DIMENSIONAL GEOMETRY

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise MULTIPLE CHOICE QUESTIONS|8 Videos

  • VECTORS

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise Multiple choice question|10 Videos

Similar Questions

Explore conceptually related problems

In triangle ABC , prove that tan((C-A)/(2))=((c-a)/(c+a))cot(B)/(2) .

In a Delta ABC, prove that tan((A+B)/(2))=cot((c)/(2))

In a triangle ABC,prove that (cot((A)/(2))+cot((B)/(2))+cot((C)/(2)))/(cot A+cot B+cot(C))=((a+b+c)^(2))/(a^(2)+b^(2)+c^(2))

If A,B,C are the interior angles of a triangle ABC, prove that (tan(B+C))/(2)=(cot A)/(2)

In any triangle ABC,prove that (a-b)/(a+b)=(tan((A-B)/(2)))/(tan((A+B)/(2)))

In any triangle ABC, prove that: (b-c)/(b+c)=(tan((b-C)/(2)))/(tan((B+C)/(2)))

In any triangle ABC, prove that: (b-c)cot(A)/(2)+(c-a)cot(B)/(2)+(a-b)cot(C)/(2)=0

In any Delta ABC, prove that :tan((A)/(2)+B)=(c+b)/(c-b)tan((A)/(2))

In triangle ABC,, prove that (tan(B-C))/(2),=[(b-c)/(b+c)](cot A)/(2)(tan(C-A))/(2),=[(c-a)/(c+a)](cot B)/(2)(tan(A-B))/(2),=[(a-b)/(a+b)](cot B)/(2)

In triangle ABC ,prove that tan(B-C)/(2)=(b-c)/(b+c)cot(A)/(2)tan(C-A)/(2)=(c-a)/(c+a)cot(B)/(2)tan(A-B)/(2)=(a-b)/(a+b)cot(C)/(2)