Bài 1: Tìm chu kỳ tuần hoàn của hàm số sau:

a) y= cos\(^2\)x                                       

Don gian bieu thuc sau

a) A= \(\dfrac{1-cosa+cos2a}{sin2a-sina}\)                         b) B= \(\sqrt{\dfrac{1}{2}-\dfrac{1}{2}\sqrt{\dfrac{1}{2}+\dfrac{1}{2}cosa}}\) (0<a≤\(\pi\)).

c) C= \(\dfrac{cosa-cos3a+cos5a-cos7a}{sina+sin3a+sin5a+sin7a}\)

Cho 0<α<π va α≠\(\dfrac{\pi}{2}\). Chung minh rang

\(\sqrt{1+cos\alpha}\) + \(\sqrt{1-cos\alpha}\) = 2sin\((\dfrac{\alpha}{2}+\dfrac{\pi}{4}\))

Chung minh rang voi moi goc luong giac α lam cho bieu thuc xac dinh thi 

a) \(\dfrac{1-sin2\alpha}{1+sin2\alpha}\)=cot\(^2\)(\(\dfrac{\pi}{4}\)+α)                 b) \(\dfrac{sin\alpha+sin\beta cos\left(\alpha+\beta\right)}{cos\alpha-sin\beta sin\left(\alpha+\beta\right)}\)=tan\(\left(\alpha+\beta\right)\).

Cho cos2x=-\(\dfrac{4}{5}\), voi \(\dfrac{\pi}{4}< x< \dfrac{\pi}{2}\). Tinh sinx, cosx, sin(x+\(\dfrac{\pi}{3}\)), cos(2x-\(\dfrac{\pi}{4}\)).