tan2x + sec2x = (cosx +sinx)/(cosx - sinx)

tan2x = sin2x/cos2x

sec2x=1/cos2x

Hence, tan2x + sec2x

(sin 2x/cos 2x) +(1/ cos 2x)

= (1+ sin 2x)/cos 2x

= (sin ^2 x + cos^2 x + 2 sin x cos x)/(cos^2 x - sin ^2x)

= (sin x+ coxs x)^2 /((cos x + sin x)( cosx - sin x))

= (sin x+ cos x) /(cos x- sin x)

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