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(1 + sin x)/(cos x) + (cos x)/(1 + sin x) = (4 sin x)/(sin 2x)

Show that left equals right, and sin 2x is a double-angle identity. I despise Trig, haha.

 Feb 29, 2016
 #1
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(1 + sin x)/(cos x) + (cos x)/(1 + sin x) = (4 sin x)/(sin 2x) {nl} Show that left equals right, and sin 2x is a double-angle identity. I despise Trig, haha.

 

1+sin(x)cos(x)+cos(x)1+sin(x)?=4sin(x)sin(2x)|sin(2x)=2sin(x)cos(x)?=4sin(x)2sin(x)cos(x)?=2cos(x)1+sin(x)cos(x)+cos(x)1+sin(x)?=2cos(x)[1+sin(x)]2+[cos2(x)]cos(x)[1+sin(x)]?=2cos(x)1+2sin(x)+sin(x)2+cos2(x)cos(x)[1+sin(x)]?=2cos(x)|sin(x)2+cos2(x)=11+2sin(x)+1cos(x)[1+sin(x)]?=2cos(x)2+2sin(x)cos(x)[1+sin(x)]?=2cos(x)2[1+sin(x)]cos(x)[1+sin(x)]?=2cos(x)2cos(x)=2cos(x)

 

laugh

 Mar 1, 2016
edited by heureka  Mar 1, 2016

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