Question

Вычеслить:cos600°-2sin²135°+cos²150°

Answer 1

$cos600^{0} -2sin^{2} 135^{0} + cos^{2} 150^{0} = \ = cos(360^{0} + 240^{0}) - 2sin^{2} (90^{0} + 45^{0} )+ cos^{2} (90 ^{0} + 60^{0}) = \ = cos240^{0} -2cos^{2} 45^{0} + sin^{2} 60^{0} = \ = cos(180^{0} + 60^{0} ) -2cos^{2} 45^{0} + sin^{2} 60^{0} = \ = - cos60^{0} -2cos^{2} 45^{0} + sin^{2} 60^{0} = \ = - frac{1}{2} - 2 times frac{ sqrt{2} }{2} times frac{ sqrt{2} }{2} + frac{ sqrt{3} }{2} times frac{ sqrt{3} }{2} = \ = - frac{1}{2} - 1 + frac{3}{4} = frac{ - 2 - 4 + 3}{4} = - frac{3}{4}$