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Section 7.1

Substitution table

Radical	Substitution	Resulting identity
$a^{2} - x^{2}$	$x = a sin θ$	$a^{2} - x^{2} = a cos θ$
$a^{2} + x^{2}$	$x = a tan θ$	$a^{2} + x^{2} = a sec θ$
$x^{2} - a^{2}$	$x = a sec θ$	$x^{2} - a^{2} = a tan θ$

We assume $a > 0$ and choose an interval of $θ$ compatible with the signs.