Question

Знайдіть значення виразу: 1) sin² 18º + sin² 72°; 2) cos3 36º - sin³ 54°.​

Answer 1

$\sin^2 18 ^{\circ} +\sin^2 72 ^{\circ} =\sin^2 18 ^{\circ} +\cos ^2 (90 ^{\circ} -72 ^{\circ} )=\\=\sin^2 18 ^{\circ} +\cos^2 18 ^{\circ} =1\\\cos ^3 36 ^{\circ} -\sin^3 54 ^{\circ} =\cos ^3 36 ^{\circ} -\sin^3 (90 ^{\circ} -54 ^{\circ} )=\\=\cos^336 ^{\circ} -\cos^3 36 ^{\circ} =0$

Answer 2

***

1) $sin^{2} 18^{0} + sin^{2} 72^{0} = sin^{2} (90^{0} - 72^{0} ) + sin^{2} 72^{0} = cos^{3} 72^{0} + sin^{2} 72^{0} = 1$

2) $cos^{3} 36^{0} - sin^{3} 54^{0} = cos^{3} (90^{0} -54^{0} ) - sin^{3} 54^{0} = sin^{3} 54^{0} - sin^{3} 54^{0} = 0$