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Trigonometric Ratio and Identites question

2025 · 28 Jan · Shift 2 · Q40
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Trigonometric Ratio and Identites question

2025 · 28 Jan · Shift 2 · Q40

JEE MainMathematicsTrigonometric Ratio and IdentitesMCQ+4 / −1
If ∑r=113{1sin⁡(π4+(r−1)π6)sin⁡(π4+rπ6)}=a3+b,a,b∈Z\sum\limits_{r=1}^{13}\left\{\frac{1}{\sin \left(\frac{\pi}{4}+(r-1) \frac{\pi}{6}\right) \sin \left(\frac{\pi}{4}+\frac{r \pi}{6}\right)}\right\}=a \sqrt{3}+b, a, b \in Zr=1∑13​{sin(4π​+(r−1)6π​)sin(4π​+6rπ​)1​}=a3​+b,a,b∈Z, then a2+b2a^2+b^2a2+b2 is equal to :
  1. A
    10
  2. B
    4
  3. C
    8
  4. D
    2
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