Question

[trần hữu trường thịnh]

1) Chứng minh :

a) \(\frac{1+\cot a}{1-\cot a}=\frac{\tan a+1}{\tan a-1}\)

b)\(\frac{\sin^2a-\cos^2a+\cos^4a}{\cos^2a-\sin^2a+sin^2a}=\tan^4a\)

2) Cho hình thang ABCD (AB//CD), góc C = 30⁰ ; góc D = 60⁰ ; AB = 1 ; CD = 5 . Tính diện tích hình thang ABCD 

Answer 1

[cao van duc]

b,ta có :\(\frac{sin^2a-cos^2a\left(1-cos^2a\right)}{cos^2a-sin^2a\left(1-sin^2a\right)}=\frac{sin^4a}{cos^4a}\)

=>\(\frac{sin^2a-sin^2a.cos^2a}{cos^2a-sin^2a.cos^2a}=\frac{sin^4a}{cos^4a}\)

=>\(\frac{sin^2a\left(1-cos^2a\right)}{cos^2a\left(1-sin^2a\right)}=\frac{sin^4a}{cos^4a}\)

=>\(\frac{sin^4a}{cos^4a}=\frac{sin^4a}{cos^4a}\)luon dung => dpcm