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Q.

If 2|sin⁡2α|=|tan⁡β+cot⁡β|,α,β∈π2,π, then the value of α+β is

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a

3π4

b

π

c

3π2

d

5π4

answer is C.

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Detailed Solution

2|sin⁡2α|≤2 and  |tan⁡β+cot⁡β|=1|sin⁡βcos⁡β|=2|cosec⁡2β|≥2∴ 2|sin⁡2α|=|tan⁡β+cot⁡β|=2∴ α=β=3π4
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If 2|sin⁡2α|=|tan⁡β+cot⁡β|,α,β∈π2,π, then the value of α+β is