Giúp tôi mấy bài này
1/ Rút gọn biểu thức:
A = 3($sin^{4}x$+$cosx^{4}x$) - 2($sin^{6}x$+$cosx^{6}x$)

B = $\frac{1+cos^{2}x}{1-cos^{2}x}$-$2cot^{2}x$

2/CMR:

$\frac{sin^{2}x-tan^{2}x}{cos^{2}x-cot^{2}x} = tan^{6}x$ (Với x là giá trị làm cho biểu thức có nghĩa)


$tan^{2}x$-$sin^{2}x$ = $tan^{2}x$.$sin^{2}x$
Giúp cái đi ạ... :) –  Lê Lê 30-04-16 01:37 PM
1
A = 3(sin⁴ x+cos⁴ x) - 2(sin⁶ x+cos⁶x)

sin⁴ x+cos⁴ x = (sin² x + cos² x)² - 2sin²x.cos²x = 1 - 2sin²x.cos²x

sin⁶ x+cos⁶x = (sin² x + cos² x)(sin⁴ x+cos⁴ x - sin²x.cos²x)
=sin⁴ x+cos⁴ x - sin²x.cos²x = 1 - 3sin²x.cos²x

  = 3(1 - 2sin²x.cos²x ) - 2(1 - 3sin²x.cos²x ) = 3 - 2 - 6sin²x.cos²x + 6sin²x.cos²x = 1

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