Question

If sin A - cos A = 1/2 find sinA + cosA

Answer 1

sinA+cosA =1/2

so,

(sinA + cosA)2 =(1/2)2

or sin2A +cos2A -2sinA*cosA =1/4................(i)

or 1- 2sinA*cosA=1/4 [sin2A +cos2A =1]

or - 2sinA*cosA=1/4-1

or 2sinA*cosA = 3/4 .............(ii)

so, from (i)

(sin2A+ cos2A) -2sinA*cosA =1/4

(sin2A+ cos2A) - 3/4 =1/4

(sinA-cosA)2 -2sinA*cosA = 1/4+3/4

(sinA+cosA)2 -(3/4) =4/4

(sinA +cosA)2 = 4/4+3/4

=7/4

(sinA +cosA) =root (7/4)

(sinA +cosA) =root7/2

so sinA+cosA =root7/2

you will better understand by writing