Value of 2sin2⁡π6+cosec2⁡7π6⋅cos2⁡π3 is mm−1. The value of 'm' is

2sin2⁡π6+cosec2⁡7π6cos2⁡π3=2×122+cosec2⁡π+π6cos2⁡π3=24+cosec2⁡π6cos2⁡π3=12+(2)2122=32=mm−1∴m=3

Value of 2sin2⁡π6+cosec2⁡7π6⋅cos2⁡π3 is mm−1. The value of 'm' is

2sin2⁡π6+cosec2⁡7π6cos2⁡π3=2×122+cosec2⁡π+π6cos2⁡π3=24+cosec2⁡π6cos2⁡π3=12+(2)2122=32=mm−1∴m=3

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Value of $2 \sin^{2} \frac{π}{6} + {cosec}^{2} \frac{7 π}{6} \cdot \cos^{2} \frac{π}{3} is \frac{m}{m - 1} .$ The value of 'm' is

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Detailed Solution

$\begin{array}{l} 2 \sin^{2} \frac{π}{6} + {cosec}^{2} \frac{7 π}{6} \cos^{2} \frac{π}{3} \\ = 2 \times {(\frac{1}{2})}^{2} + {cosec}^{2} (π + \frac{π}{6}) \cos^{2} \frac{π}{3} \\ = \frac{2}{4} + {cosec}^{2} \frac{π}{6} \cos^{2} \frac{π}{3} \\ = \frac{1}{2} + (2)^{2} {(\frac{1}{2})}^{2} = \frac{3}{2} = \frac{m}{m - 1} ∴ m = 3 \end{array}$