$sin^{2}18^{\circ}+sin^{2}36^{\circ}+sin^{2}54^{\circ}+sin^{2}72^{\circ}$ এর মান কত?

$sin^{2}18^{\circ}+sin^{2}36^{\circ}+sin^{2}54^{\circ}+sin^{2}72^{\circ}$ আমরা জানি, $sin(90^{\circ}-x) = cos(x)$ . অতএব, $sin^{2}54^{\circ} = sin^{2}(90^{\circ}-36^{\circ}) = cos^{2}36^{\circ}$ এবং $sin^{2}72^{\circ} = sin^{2}(90^{\circ}-18^{\circ}) = cos^{2}18^{\circ}$ সুতরাং, রাশিটি দাঁড়ায়: $sin^{2}18^{\circ}+sin^{2}36^{\circ}+cos^{2}36^{\circ}+cos^{2}18^{\circ}$ আমরা জানি, $sin^{2}x + cos^{2}x = 1$ . অতএব, $(sin^{2}18^{\circ}+cos^{2}18^{\circ}) + (sin^{2}36^{\circ}+cos^{2}36^{\circ})$ $= 1 + 1$ $= 2$