Question

If cos X - sin X = 1/2 then find the value of cos2x. plz answer fast ​

Answer 1

Answer:

squaring both sides, 1-Sin2X =1/4

Step-by-step explanation:

Sin2X = 3/4

hence cos2X is root7/4

Answer 2

Question :

If cos x - sin x = 1/2 , then find the value of cos2x.

Answer :

cos 2 x = √ 7 / 4

Given :

The equation cos x - sin x = 1/2

To find :

The value of cos2x

Solution :

Since cos x - sin x = 1/2

Hence, (cos x - sin x) ^2 = (1/2)^2

=> cos^2 x + sin^2 x - 2 cos x sin x = 1/4

=> 1 - sin 2 x = 1/4

=> sin 2 x = 1 - 1/4

=> sin 2 x = (4-1)/4

=> sin 2 x = 3 / 4

=> cos 2 x = √ ( 1 - sin^2 2 x)

=> cos 2 x = √ (1- (3/4)^2)

=> cos 2 x = √ (1 - 9/16)

=> cos 2 x = √ (16-9)/16

=> cos 2 x = √ (7 / 16)

=> cos 2 x = √ 7 / 4

Hence, cos 2 x = √ 7 / 4

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