How do you prove # 2tan(x)sec(x) = 1/(1-sin(x)) - 1/(1+sin(x)) #?

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Answer 1 · 2015-12-06T04:49:32

#1/(1-sin(x))-1/(1+sin(x))=2tan(x)sec(x)#

Modify only the left side, trying to make it equal #2tan(x)sec(x)#.

#1/(1-sin(x))-1/(1+sin(x))#

#=1/(1-sin(x))((1+sin(x))/(1+sin(x)))-1/(1+sin(x))((1-sin(x))/(1-sin(x)))#

#=(1+sin(x)-(1-sin(x)))/(1-sin^2x)#

#=(2sin(x))/(cos^2x)#

#=2(sin(x)/cos(x))(1/cos(x))#

#=2tan(x)sec(x)#