Question

If sinA-cosA=1/2 find sinA+cosA

Answer 1

we have sin A - cos A = 1/2

by squaring both the sides,


(sinA- cosA)^2 = (1/2)^2

sin^2A - 2 sinAcosA + cos^2A = 1/4

now we know that
sin^2 theta + cos ^2 theta = 1,

sin^2A+ cos ^2A =1,

now we have 1- 2sinAcosA = 1/4

- 2sinAcosA = 1/4-1
- 2 sinAcosA = -3/4

removing minis sign from both sides,

2sinAcosA = 3/4. (1)

now (sinA + cosA)^2 = sin^2A + 2sinAcosA + cos^2A.

= 1 + 2sinAcosA.
= 1 + 3/4. because of equation (1)
= 7/4


that's why (sinA + cos A)^2 = 7/4

taking roots

sinA + cos A = √7/2.



hope it's helpful.

All the best

Answer 2

sinA-cosA=1/2

= sin^2*A+cos^2*A-2*sinA*cosA

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

= 2*sinA*cosA=3/4 (sinA+cosA)^2=sin^2*A+cos^2*A+2*sinA*cosA =1+3/4 =7/4