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If tan theta =(tan alpha + tan beta)/(1+...

If `tan theta =(tan alpha + tan beta)/(1+tan alpha tan beta)` then show that `sin2 theta = (sin 2 alpha +sin 2 beta)/(1+sin2 alpha sin 2 beta)`

Answer

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If tan theta = ( tan alpha + tan beta)/(1 + tan alpha tan beta),"show that " sin 2 theta =(sin 2 alpha + sin 2 beta)/(1+sin 2 alpha sin 2 beta)

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Knowledge Check

  • sin alpha + sin beta = a "and" cos alpha + cos beta = b (tan alpha + tan beta)/(1-tan alpha tan beta)=

    A
    `(a^(2) + b^(2))/(2ab)`
    B
    `(b^(2)-a^(2))/(2ab)`
    C
    `(2ab)/(b^(2) + a^(2))`
    D
    `(2ab)/(b^(2) - a^(2))`

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