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

$costheta/(1+sintheta)+(1+sintheta)/costheta$

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

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

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

$=2/costheta=2sectheta$