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 $2tan(x)sec(x)$ .

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

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

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

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

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

$=2tan(x)sec(x)$

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