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}

SSC CHSL 6 Dec 2015 Shift 2 Paper

Question : 126 of 200

Marks: +1, -0

Value of the expression:

{1+2 Sin 60° Cos 60°}/{Sin 60°+Cos 60°}

+{1−2 Sin 60° Cos 60°}/{Sin 60° −Cos 60°}

Solution:

Expression :

{1+2 Sin 60° Cos 60°}/{Sin 60°+Cos 60°}

+{1−2 Sin 60° Cos 60°}/{Sin 60° −Cos 60°}

{(sin ^2 60° +cos ^2 60° )+2 Sin 60° Cos 60°}/{Sin 60°+Cos 60°}

+{(sin ^2 60° +cos ^2 60° )-2 Sin 60° Cos 60°}/{Sin 60°-Cos 60°}

(sin 60° +cos 60° )^ 2/{sin 60° +cos 60°}

+{(sin 60° -cos 60°)}^2/{sin 60° -cos 60°}

(sin 60° + cos 60° )

+ (sin 60 ° − cos 60° )

2sin 60°

2×√3/2= √3

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