Identify the expression that completes the equation so that it is an identity. cos x/1+sin x = ?

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Answer 1 · 2018-02-06T12:29:05

#secx-tanx#

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

Multiply by #1-sin(x)#

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

#color(red)(bb(1-sin^2x=cos^2x))color(white)(88)# Pythagorean identity

#((1-sinx)cosx)/(cos^2x)=(1-sinx)/cosx=1/cosx-sinx/cosx#

Identities:

#color(red)(bb(1/cosx=secx))# ,#color(white)(8888)color(red)(bb(sinx/cosx=tanx))#

#secx-tanx#

#:.#

#cos(x)/(1+sin(x))-=secx-tanx#