Dana jest liczba M= (sin 15° + sin 75°) do potęgi 2 -2 cos75°cos15.Liczba M po uproszczeniu przyjmuje wartość :

A. 1

B.-1

C. 1+2sin75°cos15°

D.( Cos° 75°-cos15°) do potęgi 2



Odpowiedź :

ZbiorJ

[tex]M=(sin15^{0} +sin75^{0} )^{2} -2cos75^{0} cos15^{0} \\\\sin15^{0}=sin(90^{0} -75^{0} )=cos75^{0}\\\\cos15^{0}=cos(90^{0} -75^{0} )=sin75^{0}\\\\podstawiam:\\\\M=(cos75^{0} +sin75^{0} )^{2} -2cos75^{0} sin75^{0} \\\\M=cos^{2} 75^{0}+2cos75^{0} sin75^{0}+ sin^{2} 75^{0} -2cos75^{0} sin75^{0}\\\\M=cos^{2} 75^{0}+ sin^{2} 75^{0} ~~~\land~~sin^{2} \alpha +cos^{2} \alpha =1~~\Rightarrow~~M=1\\\\Odp:~~A.~~1[/tex]