Question

Rút gọn
a) A= \(\frac{4sin^2a}{1-cos^2\frac{a}{2}}\)

b) B= \(\frac{1+cosa-sina }{1-cosa-sina}\)

c) C= \(\frac{1+sina-2sin^2\left(45-\frac{\pi}{2}\right)}{4cos\frac{a}{2}}\)

Answer 1

Lời giải:

a)

\(A=\frac{4\sin ^2a}{1-\cos ^2\frac{a}{2}}=\frac{4\sin ^2a}{\sin ^2\frac{a}{2}}=\frac{4(2\sin \frac{a}{2}\cos \frac{a}{2})^2}{\sin ^2\frac{a}{2}}=16\cos ^2\frac{a}{2}\)

b)

Sử dụng công thức: \(1-\cos 2a=2\sin ^2a; 1+\cos 2a=2\cos ^2a\) và \(\sin 2a=2\sin a\cos a\) ta có:

\(B=\frac{1+\cos a-\sin a}{1-\cos a-\sin a}=\frac{2\cos ^2\frac{a}{2}-2\sin \frac{a}{2}\cos \frac{a}{2}}{2\sin ^2\frac{a}{2}-2\sin \frac{a}{2}.\cos \frac{a}{2}}\)

\(=\frac{2\cos \frac{a}{2}(\cos \frac{a}{2}-\sin \frac{a}{2})}{2\sin \frac{a}{2}(\sin \frac{a}{2}-\cos \frac{a}{2})}\)

\(=\frac{-\cos \frac{a}{2}}{\sin \frac{a}{2}}=-\cot \frac{a}{2}\)

c) \(45-\frac{\pi}{2}\)??? sao đơn vị nó không thống nhất vậy?