Question #71076

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Answer 1 · 2017-02-27T21:20:07

see below

Left Hand Side:
$cos v/(1+sinv) + (1+sin v)/cos v = (cos v * cos v+(1+sinv)*(1+sinv))/(cos v(1+sin v)$

$=(cos^2v+1+2sinv+sin^2v)/(cos v(1+sin v))$

$=(cos^2v+sin^2v+1+2sinv)/(cos v(1+sin v))$

$=(1+1+2sinv)/(cos v(1+sin v))$

$=(2+2sinv)/(cos v(1+sin v))$

$=(2(1+sinv))/(cos v(1+sin v))$

$=(2(cancel (1+sinv)))/(cos v cancel((1+sin v)))$

$=2/cos v$

$=2*1/cosv$

$=2 sec v$

$:.=$ Right Hand Side