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If tanA-tanB=x a n dcotB-cotA=y , prove...

If `tanA-tanB=x a n dcotB-cotA=y ,` prove that `cot(A-B)=1/x+1/y`

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To prove that \( \cot(A - B) = \frac{1}{x} + \frac{1}{y} \) given that \( \tan A - \tan B = x \) and \( \cot B - \cot A = y \), we can follow these steps: ### Step 1: Write down the given conditions We have: 1. \( \tan A - \tan B = x \) (1) 2. \( \cot B - \cot A = y \) (2) ### Step 2: Rewrite the second condition in terms of tangent ...
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(i) If tanA-tan B=x and cot B- cot A=y . Prove that cot(A-B)=1/x + 1/y . (ii) If 2 cos A = x+1/x, 2 cos B = y + 1/y , then show that 2 cos (A-B)= x/y+y/x .

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Knowledge Check

  • If tanA-tanB=x and cotB-cotA=y , then cot(A-B)=?

    A
    `(1)/(x)+y`
    B
    `(1)/(xy)`
    C
    `(1)/(x)-(1)/(y)`
    D
    `(1)/(x)+(1)/(y)`

  • If tan A-tanB=x and cotB-cotA=y , then the value of cot(A-B) is

    A
    `(x-y)/(xy)`
    B
    `(1)/(x^(2))+(1)/(y^(2))`
    C
    `(x+y)/(xy)`
    D
    `xy`

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