chứng minh 2(1-sin@)(1+cos@)=(1-sin@+cos@)^2 13/10/2021 Bởi Valerie chứng minh 2(1-sin@)(1+cos@)=(1-sin@+cos@)^2
VT= 2-2sina +2cosa -2sinacosa =2sin²a + 2cos²a-2sina+2cosa-2sinacosa =(sina – cosa)² -2.(sina-cosa) +1 =(sina-cosa-1)²=(1-sina+cosa)²=VP – > đpcm Bình luận
$VT= 2(1-\sin a)(1+\cos a)$ $= (2-2\sin a)(1+\cos a)$ $= 2+2\cos a -2\sin a -2\sin a.\cos a$ $VP=(1-\sin a +\cos a)(1-\sin a+\cos a)$ $= 1-\sin^2a + \cos a – \sin a + \sin^2a -\sin a.\cos a + \cos a – \sin a.\cos a +\cos^2a$ $= 2+2\cos a – 2\sin a-2\sin a.\cos a$ (đpcm) Bình luận
VT= 2-2sina +2cosa -2sinacosa
=2sin²a + 2cos²a-2sina+2cosa-2sinacosa
=(sina – cosa)² -2.(sina-cosa) +1
=(sina-cosa-1)²=(1-sina+cosa)²=VP – > đpcm
$VT= 2(1-\sin a)(1+\cos a)$
$= (2-2\sin a)(1+\cos a)$
$= 2+2\cos a -2\sin a -2\sin a.\cos a$
$VP=(1-\sin a +\cos a)(1-\sin a+\cos a)$
$= 1-\sin^2a + \cos a – \sin a + \sin^2a -\sin a.\cos a + \cos a – \sin a.\cos a +\cos^2a$
$= 2+2\cos a – 2\sin a-2\sin a.\cos a$ (đpcm)