How do you simplify sec(tan-1x)?
Simplify the given expression using the trigonometric identities.
We have to evaluate sec(tan-1x)
Let's assume that
y=(tan-1x)⇒x=tany⇒x=sinycosy⇒x2=(siny)2(cosy)2⇒x2+1=cos2y+sin2ycos2y[sin2x+cos2x=1]⇒x2+1=sec2y⇒x2+1=sec2y⇒x2+1=sec(tan-1x)⇒sec(tan-1x)=x2+1
Hence, the required answer is sec(tan-1x)=x2+1