giải chi tiết hộ em vs ak

Giải thích các bước giải:

10) $\dfrac{{{{\sin }^2}a - co{s^2}a}}{{1 + 2\sin a\cos a}} = \dfrac{{1 - \cot a}}{{1 + \cot a}}$

Xét `VT=\frac{sin^a-cos^a}{1+2sinacosa}`

$\begin{array}{l} = \dfrac{{(\sin a - \cos a)(\sin a + \cos a)}}{{{{\sin }^2}a + cos{}^2a + 2\sin a\cos a}}\\ = \dfrac{{(\sin a - \cos a)(\sin a + \cos a)}}{{{{(\sin a + \cos a)}^2}}}\\ = \dfrac{{sina - \cos a}}{{sina + \cos a}} \end{array}$

$VP = \dfrac{{1 - \cot a}}{{1 + \cot a}} = \dfrac{{1 - \dfrac{{cosa}}{{\sin a}}}}{{1 + \dfrac{{\cos a}}{{\sin a}}}} = \dfrac{{\dfrac{{\sin a - cosa}}{{\sin a}}}}{{\dfrac{{\sin a + cosa}}{{\sin a}}}} = \dfrac{{\sin a - cosa}}{{\sin a + cosa}}$

Vậy `VT=VP`

11) ${\cot ^2}a - co{s^2}a = {\cot ^2}aco{s^2}a$

Xét 

$\begin{array}{l} VP = {\cot ^2}aco{s^2}a\\ = \dfrac{{{\rm{co}}{{\rm{s}}^2}a}}{{{{\sin }^2}a}}.(1 - {\sin ^2}a)\\ = \dfrac{{{\rm{co}}{{\rm{s}}^2}a}}{{{{\sin }^2}a}} - \dfrac{{{\rm{si}}{{\rm{n}}^2}{\rm{aco}}{{\rm{s}}^2}a}}{{{{\sin }^2}a}}\\ = {\cot ^2}a - co{s^2}a = VT \end{array}$