Question #18ea9

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Answer 1 · 2016-12-12T08:41:27

$R H S = 1 + \frac{2 cos x (1 + cos x)}{{sin}^{2} x}$ $RHS=1+(2cosx(1+cosx))/sin^2x$

$= 1 + \frac{2 cos x (1 + cos x)}{1 - {cos}^{2} x}$ $=1+(2cosx(1+cosx))/(1-cos^2x)$

$= 1 + \frac{2 cos x (1 + cos x)}{(1 - cos x) (1 + cos x)}$ $=1+(2cosx(1+cosx))/((1-cosx)(1+cosx))$

$=1+(2cosxcancel((1+cosx)))/((1-cosx)cancel((1+cosx)))$

$=1+(2cosx)/(1-cosx)$

$=(1-cosx+2cosx)/(1-cosx)$

$=(1+cosx)/(1-cosx)=LHS$

Proved