Question #ccc87

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Answer 1 · 2016-09-22T03:45:50

#costheta/(1+sintheta)+(1+sintheta)/costheta#

#=(costheta(1-sintheta))/((1-sintheta)(1+sintheta))+(1+sintheta)/costheta#

#=(costheta(1-sintheta))/(1-sin^2theta)+(1+sintheta)/costheta#

#=(costheta(1-sintheta))/cos^2theta+(1+sintheta)/costheta#

#=(1-sintheta)/costheta+(1+sintheta)/costheta#

#=1/costheta-sintheta/costheta+1/costheta+sintheta/costheta#

#=2/costheta=2sectheta#

Alternative

#costheta/(1+sintheta)+(1+sintheta)/costheta#

#=(cos^2theta+(1+sintheta)^2)/((1+sintheta)costheta)#

#=(cos^2theta+(1+2sintheta+sin^2theta))/((1+sintheta)costheta)#

#=(2+2sintheta)/((1+sintheta)costheta)#

#=2/costheta=2sectheta#