Simplify 2sin(x/2)cos(x/2) by using the half angle identity?

👨🏻‍🏫 學術台數學

[匿名]

2016-06-25 9:50 pm

I keep coming up with (1-cos^2)/2 which is wrong.

回答 (3)

fooks

2016-06-25 10:00 pm

Identity : sin(2θ) = 2 sin(θ) cos(θ)

Then, 2 sin(x/2) cos(x/2) = sin[2(x/2)]
Hence, 2 sin(x/2) cos(x/2) = sin(x)

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[匿名]

2016-06-25 10:05 pm

because the answer is sin(x)

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用戶48836

2016-06-25 10:09 pm

a)
x = 2t
t = x/2
sin(2t) = 2 sin(t) cos(t)
sin(x) = 2 sin(x/2) cos(x/2)

b)
sin²(x)+cos²(x) = 1
1-cos²(x) = sin²(x)

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