prove that :?

[匿名]

2016-06-21 4:52 pm

let a = cos 2x + isin 2x , b= cos2x + isin 2x .
where x1 - x2 belong to )0 /, pi/2( ,,, prove that :
1-a+b = cos(x1-x2)(cos(x1+x2)+i sin (x1+x2)

更新1:

let a = cos 2x + isin 2x , b= cos2x + isin 2x . where x1 - x2 belong to )0 /, pi/2( ,,, prove that : a+b = cos(x1-x2)(cos(x1+x2)+i sin (x1+x2)

回答 (2)

fooks

2016-06-21 5:14 pm

✔ 最佳答案

a = cos 2x₁ + i sin 2x₁
b = cos 2x₂ + i sin 2x₂

a + b
= (cos 2x₁ + i sin 2x₁) + (cos 2x₂ + i sin 2x₂)
= (cos 2x₁ + cos 2x₂) + i (sin 2x₁ + sin 2x₂)

But cos A + cos B = 2 cos [(A + B)/2] cos [(A - B)/2]
and sin A + cos B = 2 sin [(A + B)/2] cos [(A - B)/2]

Hence, a + b
= (cos 2x₁ + cos 2x₂) + i (sin 2x₁ + sin 2x₂)
= 2 cos [(2x₁ + 2x₂)/2] cos [(2x₁ - 2x₂)/2] + 2i sin [(2x₁ + 2x₂)/2] cos [(2x₁ - 2x₂)/2]
= 2 cos (x₁ + x₂) cos (x₁ - x₂) + 2i sin (x₁ + x₂) cos (x₁ - x₂)
= 2 cos (x₁ - x₂) [cos (x₁ + x₂) + i sin (x₁ + x₂)]

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[匿名]

2016-06-21 4:53 pm

DO YOUR OWN WORK.

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