Rút gọn biểu thức
A = sin^2 30 – sin^ 40 – sin^2 50 + sin^2 60
B = cos^2 25 – cos^2 35 + cos^2 45 – cos^2 55 + cos^2 65
Rút gọn biểu thức A = sin^2 30 – sin^ 40 – sin^2 50 + sin^2 60 B = cos^2 25 – cos^2 35 + cos^2 45 – cos^2 55 + cos^2 65
By Kylie
$A=\sin^230^o+\sin^260^-(\sin^240^o+\sin^250^o)$
$=\sin^230^o+\cos^230^o-(\sin^240^o+\cos^240^o)$
$=1-1=0$
$B=\cos^225^o+\cos^265^o-(\cos^235^o+\cos^255^o)+\cos^245^o$
$=\cos^225^o+\sin^225^o-(\sin^255^o+\cos^255^o)+(\dfrac{1}{\sqrt2})^2$
$=1-1+\dfrac{1}{2}$
$=\dfrac{1}{2}$
Đáp án:
Giải thích các bước giải:
`A = sin^2 30^o- sin^2 40^o – sin^2 50^o + sin^2 60^o`
`A=sin^2 30^o- sin^2 40^o – cos^2 40^o + cos^2 30^o`
`A=(sin^2 30^o + cos^2 30^o) – (sin^2 40^o + cos^2 40^o)`.
`A=1-1`
`A=0`.
`B = cos^2 25^o – cos^2 35^o + cos^2 45^o – cos^2 55^o + cos^2 65^o`
`B = cos^2 25^o – cos^2 35^o + cos^2 45^o – sin^2 35^o + sin^2 25^o`
`B = (cos^2 25^o + sin^2 25^o) – (cos^2 35^o + sin^2 35^o) + cos^2 45^o`
`B = 1 – 1 + 1/2`
`B=1/2`.