Question

if Sin A + cos A =√5/2 then find the value of Cos A - sin A=​

Answer 1

Answer:

Sin A + cos A =√5/2

(Sin A + cos A)² =(√5/2)²

sin²A+cos²A+2sinAcosA=5/4 (sin²A+cos²A=1)

1+2sinAcosA=5/4

2sinAcosA=5/4 -1=5-4/4=1/4

sinAcosA=1/4 ×1/2=1/8

(cosA-sinA)²=cos²A+sin²A-2sinAcosA

=1-2(1/8)=1 -1/4 =4-1/4=3/4

cosA-sinA=√3/4=√3/2

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