How do you perform addition or subtraction and use the fundamental identities to simplify $cosx/(1+sinx)+(1+sinx)/cosx$ ?

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Answer 1 · 2017-01-14T09:12:11

$2secx.$

The Exp. $=cosx/(1+sinx)+(1+sinx)/cosx$

$={cos^2x+(1+sinx)^2}/{(1+sinx)cosx}$

$=(cos^2x+1+2sinx+sin^2x)/{(1+sinx)cosx}$

$={2(1+sinx)}/{(1+sinx)cosx}....[because, cos^2x+sin^2x=1]$

$=2secx.$

How do you perform addition or subtraction and use the fundamental identities to simplify cosx/(1+sinx)+(1+sinx)/cosxcosx/(1+sinx)+(1+sinx)/cosx?