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Prove that tan.(A)/(2)+tan.(B)/(2)+tan.(...

Prove that `tan.(A)/(2)+tan.(B)/(2)+tan.(C)/(2)=(bc+ca+ab-s^(2))/(Delta)`

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Prove that (ii) tan"" (A)/(2) + tan"" (B)/(2) + tan"" (C )/(2) = (bc + ca + ab - s^2)/( Delta )

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Knowledge Check

  • Assertion (A) : If alpha = 12^@, beta = 15^@ , gamma=18^@ then tan 2 alpha tan 2 beta + tan beta tan 2 gamma + tan 2 gamma tan 2 alpha =1 Reason (R ): in Delta ABC, tan. (A)/(2) tan.(B)/(2) tan .(C )/(2) + tan.(C )/(2) tan.(A)/(2)= Which of the following is true?

    A
    Both (A) and (R ) are true and (R ) is the correct explanation of (A)
    B
    Both (A) and (R ) are true, but (R ) is not the correct explanation of (A)
    C
    (A) is true, but (R ) is false
    D
    (A) is false, but (R ) is true

  • If Delta ABC , if x = tan((B-C)/(2)) tan.(A)/(2), y = tan((C-A)/(2)) tan.(B)/(2) and z = tan((A-B)/(2))tan.(C )/(2) , then (x + y + z) =

    A
    xyz
    B
    `-xyz`
    C
    `2xyz`
    D
    `(1)/(2) xyz`

  • In Delta ABC, tan""(A)/(2)+tan ""(B)/(2)=

    A
    `(c cot ""(C)/(2))/(4s)`
    B
    `(2c cot ""(C)/(2))/(a+b+c)`
    C
    `(2c tan ""(C)/(2))/(s)`
    D
    `(c tan ""(C)/(2))/(a+b+c)`

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    In DeltaABC , tan""((A+B)/(2))*tan""(C)/(2)=

    Assertion (A) If alpha =12 ^(@),beta = 15^(@),gamma = 18^(@) , then tan 2 alpha tan 2beta + tan 2betatan 2gamma+tan2gamma tan 2alpha=1 Reason ( R ) In DeltaABC, " tan "(A)/(2) " tan " (B)/(2)+ " tan " (B)/(2) " tan " (C)/(2) + " tan "(C)/(2) " tan "(A)/(2)=1 Which of the following is true?

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    In Delta ABC , if x=tan((B-C)/(2))tan.(A)/(2),y=tan((C-A)/(2))tan.(B)/(2) and z=tan((A-B)/(2))tan.(C)/(2) then (x+y+z)= .

    In Delta ABC ( tan ""(A)/(2) - tan ""(B) /(2)) /( tan ""(A)/(2) +tan ""(B)/(2)) =

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