Question

[Nguyễn Hồng Nhung]

Bài 1: Thu gọn
a) A= sin²\(\alpha\) + sin²\(\alpha\) . tan\(\alpha\)

b) B= \(\dfrac{1+2.sin\alpha.cos\alpha}{sin\alpha+cós\alpha}\)- cos\(\alpha\)

c) C= cos\(\alpha\) + \(\dfrac{sin\alpha}{1+cos\alpha}\)

Answer 1

[Nguyễn Lê Phước Thịnh]

a: Sửa đề: \(A=sin^2a+sin^2a\cdot tan^2a\)

\(=sin^2a\left(1+tan^2a\right)=sin^2a\cdot\dfrac{1}{cos^2a}=tan^2a\)

b: \(=\dfrac{\left(sina+cosa\right)^2}{sina+cosa}-cosa=sina+cosa-cosa=sina\)

c: \(=\dfrac{cosa+cos^2a+sina}{1+cosa}\)