Chứng minh rằng (sin^2 a + cos^2 a)^2 – (sin^2 a – cos^2 a)^2/ sin a. cos a = 4 giải giúp em với ạ 09/07/2021 Bởi Maya Chứng minh rằng (sin^2 a + cos^2 a)^2 – (sin^2 a – cos^2 a)^2/ sin a. cos a = 4 giải giúp em với ạ
$\dfrac{(\sin a + \cos a)^2 – (\sin a – \cos a)^2}{\sin a\cos a}$ $= \dfrac{\sin^2a + \cos^2a + 2\sin a\cos a – (\sin^2 + \cos^2x – 2\sin x\cos x)}{\sin a\cos a}$ $=\dfrac{1 + 2\sin a\cos a – (1 – 2\sin a\cos a)}{\sin a\cos a}$ $= \dfrac{4\sin a\cos a}{\sin a\cos a}$ $= 4$ Bình luận
$\dfrac{(\sin^2a+\cos^2a)^2-(\sin^2a-\cos^2a)^2}{\sin a.\cos a}$ $=\dfrac{(\sin^2a+\cos^2a+\sin^2a-\cos^2a)(\sin^2a+\cos^2a-\sin^2a+\cos^2a)}{\sin a.\cos a}$ $=\dfrac{2\sin^2a.2\cos^2a}{\sin a.\cos a}$ $=\dfrac{4(sin a.\cos a)^2}{\sin a.\cos a}$ $=4\sin a.\cos a$ Bình luận
$\dfrac{(\sin a + \cos a)^2 – (\sin a – \cos a)^2}{\sin a\cos a}$
$= \dfrac{\sin^2a + \cos^2a + 2\sin a\cos a – (\sin^2 + \cos^2x – 2\sin x\cos x)}{\sin a\cos a}$
$=\dfrac{1 + 2\sin a\cos a – (1 – 2\sin a\cos a)}{\sin a\cos a}$
$= \dfrac{4\sin a\cos a}{\sin a\cos a}$
$= 4$
$\dfrac{(\sin^2a+\cos^2a)^2-(\sin^2a-\cos^2a)^2}{\sin a.\cos a}$
$=\dfrac{(\sin^2a+\cos^2a+\sin^2a-\cos^2a)(\sin^2a+\cos^2a-\sin^2a+\cos^2a)}{\sin a.\cos a}$
$=\dfrac{2\sin^2a.2\cos^2a}{\sin a.\cos a}$
$=\dfrac{4(sin a.\cos a)^2}{\sin a.\cos a}$
$=4\sin a.\cos a$