If Cos A + Sin A = \sqrt2 Cos A then Cos A- Sin A is equal to: (Where 0°

SSC CHSL 6 Dec 2015 Shift 1 Paper

Question : 130 of 200

Marks: +1, -0

If Cos A + Sin A =

√2

Cos A then Cos A- Sin A is equal to: (Where 0°

<

<

90°)

Solution:

Given :

cosA + sinA = √2cosA

Squaring both sides, we get :
⇒

(cosA + sinA)^ 2 = ( √2cosA) ^2

⇒

cos ^2A + sin^ 2A + 2sinA.cosA

= 2cos^ 2A

⇒

1 + 2sinA.cosA = 2(1 − sin^2 A)

⇒

1 + 2sinA.cosA = 2cos

= 2 − 2sin ^2A

⇒

2sinA.cosA=2cos

= 1 − 2sin ^2A

------(i)
To find :

cosA − sinA = x

Squaring both sides, we get :
⇒

x ^2 = cos ^2A + sin ^2A

− 2sinA.cosA

Substituting value from equation (i),
⇒

x ^2 = 1 − (1 − 2sin^2 A)

⇒

x^2 =2sin^ 2A

⇒

x =√ {2sin^2A}

⇒

x = √2sinA

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