LG a

Lời giải chi tiết:

\(\begin{array}{l}
\frac{{{{\sin }^3}\left( {\frac{\pi }{2} + k\pi } \right) + {{\cos }^3}\left( {\frac{\pi }{2} + k\pi } \right)}}{{2\cos \left( {\frac{\pi }{2} + k\pi } \right) - \sin \left( {\frac{\pi }{2} + k\pi } \right)}} = \cos \left[ {2\left( {\frac{\pi }{2} + k\pi } \right)} \right]\\
\Leftrightarrow \frac{{{{\left( { - 1} \right)}^{3k}} + 0}}{{2.0 - {{\left( { - 1} \right)}^k}}} = \cos \left( {\pi + k2\pi } \right)\\
\Leftrightarrow \frac{{{{\left( { - 1} \right)}^{3k}}}}{{ - {{\left( { - 1} \right)}^k}}} = \cos \pi \\
\Leftrightarrow - {\left( { - 1} \right)^{2k}} = - 1\\
\Leftrightarrow - 1 = - 1
\end{array}\)

LG b

Lời giải chi tiết:

\(\eqalign{& {{{t^3} + 1} \over {\left( {2 - t} \right)\left( {1 + {t^2}} \right)}} = {{1 - {t^2}} \over {1 + {t^2}}} \cr & \Leftrightarrow {t^3} + 1 = \left( {{t^2} - 1} \right)\left( {t - 2} \right) \cr & \Leftrightarrow {t^3} + 1 = {t^3} - 2{t^2} - t + 2 \cr & \Leftrightarrow 2{t^2} + t - 1 = 0 \Leftrightarrow \left[ {\matrix{
๊{t = - 1} \cr {t = {1 \over 2}} \cr} } \right. \cr & \Leftrightarrow \left[ {\matrix{{\tan x = - 1} \cr {\tan x = {1 \over 2}} \cr} } \right. \Leftrightarrow \left[ {\matrix{{x = - {\pi \over 4} + k\pi } \cr {x = \alpha + k\pi } \cr} } \right. \cr & \text{ với }\,\tan \alpha = {1 \over 2} \cr} \)

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