Question 126

Value of the expression: $$\frac{1+2\ Sin\ 60^\circ Cos\ 60^\circ}{Sin\ 60^\circ + Cos\ 60^\circ}+\frac{1-2\ Sin\ 60^\circ Cos\ 60^\circ}{Sin\ 60^\circ - Cos\ 60^\circ}$$

Solution

Expression : $$\frac{1+2\ Sin\ 60^\circ Cos\ 60^\circ}{Sin\ 60^\circ + Cos\ 60^\circ}+\frac{1-2\ Sin\ 60^\circ Cos\ 60^\circ}{Sin\ 60^\circ - Cos\ 60^\circ}$$

= $$\frac{(sin^2\ 60^\circ+cos^2\ 60^\circ)+2\ Sin\ 60^\circ Cos\ 60^\circ}{Sin\ 60^\circ + Cos\ 60^\circ}+\frac{(sin^2\ 60^\circ+cos^2\ 60^\circ)-2\ Sin\ 60^\circ Cos\ 60^\circ}{Sin\ 60^\circ - Cos\ 60^\circ}$$

= $$\frac{(sin\ 60^\circ+cos\ 60^\circ)^2}{sin\ 60^\circ+cos\ 60^\circ}$$ $$+\frac{(sin\ 60^\circ-cos\ 60^\circ)^2}{sin\ 60^\circ-cos\ 60^\circ}$$

= $$(sin\ 60^\circ+cos\ 60^\circ)+(sin\ 60^\circ-cos\ 60^\circ)$$

= $$2sin\ 60^\circ$$

= $$2\times\frac{\sqrt3}{2}=\sqrt3$$

=> Ans - (C)


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