A= sin ²15 + sin ²30 + sin ²45+ sin ²60+sin ²75 B= cos ²12+cos ²23+cos ²34+cos45+cos ²56+cos ²67+cos78 09/08/2021 Bởi Isabelle A= sin ²15 + sin ²30 + sin ²45+ sin ²60+sin ²75 B= cos ²12+cos ²23+cos ²34+cos45+cos ²56+cos ²67+cos78
$A=\sin^215^o+\sin^275^o+\sin^230^o+\sin^260^o+\sin^245^o$ $=\sin^215^o+\cos^215^o+\sin^230^o+\sin^230^o+\sin^245^o$ $=1+1+\dfrac{1}{2}=2,5$ $B=\cos^212^o+\cos^278^o+\cos^223^o+\cos^267^o+\cos^234^o+\cos^250^o+\cos 45^o$ Vì $\cos (90^o-x)=\sin x$, $\cos 45^o=\dfrac{1}{\sqrt2}$ $\Rightarrow B=1+1+1+\dfrac{1}{\sqrt2}$ $= \dfrac{6+\sqrt2}{2}$ Bình luận
Đáp án: ` A = 5/2` `B = 7/2` Giải thích các bước giải: `A = sin^2 15 + sin^2 30 +sin^2 45+sin^2 60 + sin^2 75` `= sin^2 15 + sin^2 30 + sin^2 45 + cos^2 30 + cos^2 15` `= (sin^2 15 +cos^2 15) + (sin^2 30 + cos^2 30) + sin^2 45` `= 1 + 1 + 1/2` `= 5/2` `B = cos^2 12 + cos^2 23 + cos^2 34 +cos^2 45 +cos^2 56 + cos^2 67 + cos^2 78` `= cos^2 12 + cos^2 23 + cos^2 34 + cos^2 45 + sin^2 34 + sin^2 23 + sin^2 12` `= (cos^2 12 + sin^2 12) + (cos^2 23 + sin^2 23) + (cos^2 34 + sin^2 34) + cos^2 45` `= 1 + 1 + 1 + 1/2` `= 7/2` Bình luận
$A=\sin^215^o+\sin^275^o+\sin^230^o+\sin^260^o+\sin^245^o$
$=\sin^215^o+\cos^215^o+\sin^230^o+\sin^230^o+\sin^245^o$
$=1+1+\dfrac{1}{2}=2,5$
$B=\cos^212^o+\cos^278^o+\cos^223^o+\cos^267^o+\cos^234^o+\cos^250^o+\cos 45^o$
Vì $\cos (90^o-x)=\sin x$, $\cos 45^o=\dfrac{1}{\sqrt2}$
$\Rightarrow B=1+1+1+\dfrac{1}{\sqrt2}$
$= \dfrac{6+\sqrt2}{2}$
Đáp án:
` A = 5/2`
`B = 7/2`
Giải thích các bước giải:
`A = sin^2 15 + sin^2 30 +sin^2 45+sin^2 60 + sin^2 75`
`= sin^2 15 + sin^2 30 + sin^2 45 + cos^2 30 + cos^2 15`
`= (sin^2 15 +cos^2 15) + (sin^2 30 + cos^2 30) + sin^2 45`
`= 1 + 1 + 1/2`
`= 5/2`
`B = cos^2 12 + cos^2 23 + cos^2 34 +cos^2 45 +cos^2 56 + cos^2 67 + cos^2 78`
`= cos^2 12 + cos^2 23 + cos^2 34 + cos^2 45 + sin^2 34 + sin^2 23 + sin^2 12`
`= (cos^2 12 + sin^2 12) + (cos^2 23 + sin^2 23) + (cos^2 34 + sin^2 34) + cos^2 45`
`= 1 + 1 + 1 + 1/2`
`= 7/2`