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Prove that (tan alpha+tan beta)/(cot alp...

Prove that `(tan alpha+tan beta)/(cot alpha+cot beta)=tan alpha tan beta`

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Knowledge Check

  • For 0 lt alpha, beta lt pi//2 , let E=(tan alpha+tan beta)(1-cot alpha cot beta)+(cot alpha+cot beta)(1-tan alpha tan beta) then E is

    A
    independent of `alpha` only
    B
    independent of `beta` only
    C
    independent of `alpha` and `beta` both
    D
    equal to `2(tan alpha+tan beta)`

  • (tan alpha + tan beta )/( tan (alpha + beta ))+(tan alpha - tan beta )/(tan (alpha - beta )) =

    A
    0
    B
    1
    C
    2
    D
    `1//2`

  • (sec alpha * sec beta + tan alpha tan beta )^(2)-( sec alpha * tan beta + tan alpha * sec beta )^(2) =

    A
    0
    B
    1
    C
    `-1`
    D
    `sqrt(2)`

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