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# Need some help with this trigo ques thanks!

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Heya

Here's the ques:

Given : sin\alpha+sin\beta=1 , cos\alpha+cos\beta=1

Find the value of sin\alpha-cos\beta

Thanks~

Guest May 13, 2017
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#1
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Given : sin\alpha+sin\beta=1 , cos\alpha+cos\beta=1

Find the value of sin\alpha-cos\beta

heureka  May 15, 2017
edited by heureka  May 15, 2017
#2
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$$\sin \alpha + \sin \beta = 1\\ \cos \alpha + \cos \beta = 1\\ 1 + 1 + 2\sin \alpha \sin \beta + 2\cos \alpha \cos \beta=2 \\\cos (\beta - \alpha) = 0\\ \beta - \alpha = \pi/2\\ \beta = \pi/2 + \alpha\\ \sin \alpha + \sin(\pi/2+\alpha)=1\\ \sin \alpha + \sin \pi/2 \cos\alpha+\cos \pi/2 \sin \alpha = 1\\ \sin \alpha + \cos \alpha = 1\\ \therefore\cos \alpha = \sin\beta\\ \therefore \alpha = \beta = \pi/4\\ \therefore \sin \alpha - \cos \beta = 0$$

MaxWong  May 15, 2017

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