Consider performing a substitution of the form x = a tan θ {\displaystyle x=a\tan \theta } for some constant a {\displaystyle a} .
Note that ( a tan θ ) 2 + a 2 = a 2 ( tan 2 θ + 1 ) = a 2 sec 2 θ = ( a sec θ ) 2 {\displaystyle (a\tan \theta )^{2}+a^{2}=a^{2}(\tan ^{2}\theta +1)=a^{2}\sec ^{2}\theta =(a\sec \theta )^{2}} .
for some constant 
.
.
