Question

plz answer this question friends ​

Answer 1

Hey Mate your answer is 1 .

Step-by-step explanation:

$\frac{ { \sin }^{2} \frac{\pi}{18} + {sin}^{2} \frac{\pi}{9} + {sin}^{2} \frac{7\pi}{18} + {sin}^{2} \frac{4\pi}{9} }{ { \cos}^{2} \frac{\pi}{18} + {cos}^{2} \frac{\pi}{9} + {cos}^{2} \frac{7\pi}{18} + {cos}^{2} \frac{4\pi}{9} } \\ \\ \frac{ { \sin }^{2} \frac{180}{18} + {sin}^{2} \frac{180}{9} + {sin}^{2} \frac{(7 \times 180)}{18} + {sin}^{2} \frac{(4 \times 180)}{9} }{ { \cos}^{2} \frac{180}{18} + {cos}^{2} \frac{180}{9} + {cos}^{2} \frac{(7 \times 180)}{18} + {cos}^{2} \frac{(4 \times 180)}{9} } \\ \\ \frac{ { \sin }^{2} 10 + {sin}^{2} 20 + {sin}^{2} 70 + {sin}^{2} 80}{ { \cos}^{2} 10 + {cos}^{2} 20+ {cos}^{2} 70+ {cos}^{2} 80} \\ \\ \frac{ { \sin }^{2} (90 - 80) + {sin}^{2} ( 90 - 70) + {sin}^{2} 70 + {sin}^{2} 80}{ { \cos}^{2} (90 - 80) + {cos}^{2} (90 - 70)+ {cos}^{2} 70+ {cos}^{2} 80} \\ \\ \frac{ { cos}^{2} 80 + {sin}^{2} 80 + {sin}^{2} 70 + {cos}^{2} 70}{ { sin}^{2} 80 + {cos}^{2} 80+ {cos}^{2} 70+ {cos}^{2} 70} \\ \frac{1 + 1}{1 + 1} \\ \frac{2}{2} \\ 1$

Using Identity

sin(90 - ∅) = cos∅

cos(90 - ∅) = sin∅

sin²∅ + cos²∅ = 1