Question

If secA - cosA = √5, find secA + cosA

Answer 1

secA - cosA =5-----(1)

(secA+ cosA)^2= (secA - co A)^2 + 4 secA cosA

=(root 5)^2+ 4* 1/cosA*cosA {from(1)}

=5+4
=9

therefore

secA+ cosA = root9

=3

Answer 2

let,
secA-cosA be a
⇒√5 and
secA=cosA be b
⇒?

we know, (a-b)square=a square+b square
so,Squaring on both sides,

(a-b)2=(√5)2

(a+b)(a-b)=5

(a+b)√5=5

(a+b)=5/√5

a+b=√5

therefore,secA+cosA=√5