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IPMAT Indore 2022

Geometry
>
Trigonometry

Hard

If sin⁡α+sin⁡β=23\sin \alpha+\sin \beta=\frac{\sqrt{2}}{\sqrt{3}} and cos⁡α+cos⁡β=13\cos \alpha+\cos \beta=\frac{1}{\sqrt{3}}, then the value of (20cos⁡(α−β2))2\left(20 \cos \left(\frac{\alpha-\beta}{2}\right)\right)^{2} is _________.

Entered answer:

Correct Answer: 100

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