Cho hình hộp chữ nhật ABCD ⋅ A ' B ' C ' D 'có đáy ABCD là hình vuông, AB =1và A A '= a ( a >0). Khi a thay đồi, tìm giá trị lớn nhất của góc tạo bởi đường thẳng B ' D và mặt phẳng BD C '.

Giải thích

D ễ th ấ y C B ' c ắ t B C ' t ạ i trung đ i ể m c ủ a m ỗ i đườ ng sin invisible function application open parentheses stack D B with rightwards arrow on top comma open parentheses B D C to the power of straight prime close parentheses close parentheses end cell row cell equals fraction numerator d open parentheses B to the power of straight prime comma open parentheses B D C to the power of straight prime close parentheses close parentheses over denominator D B to the power of straight prime end fraction equals fraction numerator 1 over denominator square root of open parentheses a squared plus b squared plus 1 close parentheses open parentheses 1 over a squared plus 1 over b squared plus 1 close parentheses end root end fraction end cell end table" class="Wirisformula" data-latex="" data-mathml="«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnspacing=¨0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em¨ columnalign=¨right left right left right left right left right left right left¨»«mtr»«mtd»«mtext»§#160;N§#234;n§#160;«/mtext»«mi»d«/mi»«mfenced separators=¨|¨»«mrow»«msup»«mi»B«/mi»«mi mathvariant=¨normal¨»§#8242;«/mi»«/msup»«mo»,«/mo»«mfenced separators=¨|¨»«mrow»«mi»B«/mi»«msup»«mi»C«/mi»«mi mathvariant=¨normal¨»§#8242;«/mi»«/msup»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo»=«/mo»«mi»d«/mi»«mfenced separators=¨|¨»«mrow»«mi»C«/mi»«mo»,«/mo»«mfenced separators=¨|¨»«mrow»«mi»B«/mi»«mi»D«/mi»«msup»«mi»C«/mi»«mi mathvariant=¨normal¨»§#8242;«/mi»«/msup»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo»=«/mo»«/mtd»«/mtr»«mtr»«mtd»«mfrac»«mn»1«/mn»«msqrt»«mfrac»«mn»1«/mn»«mrow»«mi»C«/mi»«msup»«mi»D«/mi»«mn»2«/mn»«/msup»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mn»1«/mn»«mrow»«mi»C«/mi»«msup»«mi»C«/mi»«mrow»«mi mathvariant=¨normal¨»§#8242;«/mi»«mn»2«/mn»«/mrow»«/msup»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mn»1«/mn»«mrow»«mi»C«/mi»«msup»«mi»B«/mi»«mn»2«/mn»«/msup»«/mrow»«/mfrac»«/msqrt»«/mfrac»«mo»=«/mo»«mfrac»«mn»1«/mn»«msqrt»«mn»1«/mn»«mo»+«/mo»«mfrac»«mn»1«/mn»«msup»«mi»a«/mi»«mn»2«/mn»«/msup»«/mfrac»«mo»+«/mo»«mfrac»«mn»1«/mn»«msup»«mi»b«/mi»«mn»2«/mn»«/msup»«/mfrac»«/msqrt»«/mfrac»«/mtd»«/mtr»«mtr»«mtd»«mi»D«/mi»«msup»«mi»B«/mi»«mi mathvariant=¨normal¨»§#8242;«/mi»«/msup»«mo»=«/mo»«msqrt»«msup»«mi»a«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«msup»«mi»b«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»1«/mn»«/msqrt»«mo»=§#62;«/mo»«mi»sin«/mi»«mo»§#8289;«/mo»«mfenced separators=¨|¨»«mrow»«mover accent=¨true¨»«mrow»«mi»D«/mi»«mi»B«/mi»«/mrow»«mo»§#8594;«/mo»«/mover»«mo»,«/mo»«mfenced separators=¨|¨»«mrow»«mi»B«/mi»«mi»D«/mi»«msup»«mi»C«/mi»«mi mathvariant=¨normal¨»§#8242;«/mi»«/msup»«/mrow»«/mfenced»«/mrow»«/mfenced»«/mtd»«/mtr»«mtr»«mtd»«mo»=«/mo»«mfrac»«mrow»«mi»d«/mi»«mfenced separators=¨|¨»«mrow»«msup»«mi»B«/mi»«mi 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