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(cosx + sinx) (cosx – sinx) = ab

cos2x – sin2x = ab

cos 2x = ab

sin2 2x + cos2 2x = 1

sin2 2x = 1 – cos2 2x

sin2x = ± √ 1 – (ab)

           = ± √ (1 + ab)(1 – ab)

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Hi Jieheng,

I follow your steps,  but the ans key is (a^2 -1) or (1-b^2). Pls help. Tks

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a = cos x + sin x

a² = (cos x + sin x)²

a² = cos ²x + sin²x + 2sin x cos x

a² = 1 + sin 2x

sin 2x = a² – 1 =(a+1)(a-1)

 

OR

b = cos x – sin x

b² = (cos x – sin x)²

b² = cos ²x + sin²x – 2sin x.cos x

b² = 1 – sin 2x

sin 2x = 1 – b²  =(1+b)(1-b)

 

OR

 

a+b = 2cos x ….(1)

a-b = 2sin x ….(2)

(1)*(2):

2(2sin x .cos x) = (a+b)(a-b)

sin 2x = (a+b)(a-b)/2

 

 

cheers.

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