cho tanx = $\frac{5}{7}$ . Tính p = 5tan2x + 7cos$x^{2}$

Đáp án:

 `P=\frac{8533}{444}`

Giải thích các bước giải:

Ta có: $\tan 2x = \dfrac{{2\tan x}}{{1 - {{\tan }^2}x}};\dfrac{1}{{{\rm{co}}{{\rm{s}}^2}x}} = 1 + {\tan ^2}x$

$\begin{array}{l} P = 5\tan 2x + 7{\cos ^2}x\\ = 5.\dfrac{{2\tan x}}{{1 - {{\tan }^2}x}} + 7.\dfrac{1}{{1 + {{\tan }^2}x}}\\ = 5.\dfrac{{2.\dfrac{5}{7}}}{{1 - {{\left( {\dfrac{5}{7}} \right)}^2}}} + 7.\dfrac{1}{{1 + {{\left( {\dfrac{5}{7}} \right)}^2}}}\\ = \dfrac{{8533}}{{444}} \end{array}$