Question

[Yukino Mihara]

Bài 1: Tính gt biểu thức: \(cos^220^o+cos^240^o+cos^250^o+cos^270^o\)

Bài 2:Chứng minh hệ thức:

a,\(cot^2\text{α}-cos^2\text{α}=cot^2\text{α}.cos^2\text{α}\)

b,\(\dfrac{1+cos\text{ α}}{sin\text{ α}}=\dfrac{sin\text{ α}}{1-cos\text{ α}}\)

(P/s: tại mik ko tìm đc kí hiệu Anpha nên phải viết chữ =.=)

Các bạn giúp mik vs, mik đang cần gấp ak.Mik cảm ơn!!!!

Answer 1

[Mysterious Person]

bài 1: ta có : \(cos^220+cos^240+cos^250+cos^270\)

\(=cos^220+cos^270+cos^240+cos^250\)

\(=cos^220+cos^2\left(90-20\right)+cos^240+cos^2\left(90-40\right)\)

\(=cos^220+sin^220+cos^240+sin^240=1+1=2\)

bài 2: a) ta có : \(cot^2\alpha-cos^2\alpha=cos^2\alpha\left(\dfrac{1}{sin^2\alpha}-1\right)=cos^2\alpha.\left(\dfrac{1-sin^2\alpha}{sin^2\alpha}\right)\)

\(=cos^2\alpha.\left(\dfrac{cos^2\alpha}{sin^2\alpha}\right)=cos^2\alpha.cot^2\alpha\left(đpcm\right)\)

b) ta có : \(sin^2\alpha+cos^2\alpha=1\Leftrightarrow sin^2\alpha=1-cos^2\alpha\)

\(\Leftrightarrow sin^2\alpha=\left(1-cos\alpha\right)\left(1+cos\alpha\right)\Leftrightarrow\dfrac{1+cos\alpha}{sin\alpha}=\dfrac{sin\alpha}{1-cos\alpha}\left(đpcm\right)\)

Answer 2

[Yukino Mihara]

dạ e cảm ơn nh ạ!!!!