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