Lời giải:
1.
\(\cos ^2x+\cos ^2x\tan ^2x=\cos ^2x+\cos ^2x.(\frac{\sin x}{\cos x})^2\)
\(=\cos ^2x+\sin ^2x=1\)
2.
\(\frac{2\cos ^2a-1}{\sin a+\cos a}=\frac{2\cos ^2a-(\sin ^2a+\cos ^2a)}{\sin a+\cos a}=\frac{\cos ^2a-\sin ^2a}{\sin a+\cos a}=\frac{(\cos a-\sin a)(\cos a+\sin a)}{\sin a+\cos a}\)
\(=\cos a-\sin a\)
3.
\(\frac{1-2\sin ^2a}{\sin a-\cos a}=\frac{\cos ^2a+\sin ^2a-2\sin ^2a}{\sin a-\cos a}=\frac{\cos ^2a-\sin ^2a}{\sin a-\cos a}\)
\(=\frac{(\cos a-\sin a)(\cos a+\sin a)}{\sin a-\cos a}=-(\cos a+\sin a)\)
4.
\(\frac{1+\sin a}{1-\sin a}-\frac{1-\sin a}{1+\sin a}=\frac{(1+\sin a)^2-(1-\sin a)^2}{(1-\sin a)(1+\sin a)}\)
\(=\frac{1+\sin ^2a+2\sin a-(1+\sin ^2a-2\sin a)}{1-\sin ^2a}=\frac{4\sin a}{\cos ^2a}=\frac{4\tan a}{\cos a}\)
