1. If (tanA + tanB)/(1 - tanAtanB) = x, then the value of x is
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By: anil on 05 May 2019 02.10 am
Expression : (tanA + tanB)/(1 - tanAtanB) = x = $$(frac{sin A}{cos A} + frac{sin B}{cos B}) div (1 - frac{sin A sin B}{cos A cos B})$$ = $$(frac{sin Acos B + cos Asin B}{cos Acos B}) div (frac{cos Acos B - sin Asin B}{cos Acos B})$$ = $$[frac{sin(A + B)}{cos A cos B}] div [frac{cos(A + B)}{cos A cos B}]$$ = $$[frac{sin(A + B)}{cos A cos B}] imes [frac{cos A cos B}{cos(A + B)}]$$ = $$frac{sin(A + B)}{cos(A + B)} = tan(A + B)$$ => Ans - (A)
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