If secA + tanA = a, then the value of cosA is

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secA + tanA = a ..... (i)
∵ sec²A – tan²A = 1
⇒ (secA + tanA) (secA – tanA) = 1
² secA – tanA = 1/a ... (ii)
On adding equations (i) and (ii),

2 secA = a +	1	=	a² + 1
	a		a

⇒ secA =	a² + 1
	2a

⇒ cosA =	2a
	a² + 1