Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
a,\\
A = \frac{{\sin 405^\circ + \sin 495^\circ }}{{\cos 1830^\circ + \cos 3660^\circ }}\\
= \frac{{\sin \left( {45^\circ + 360^\circ } \right) + \sin \left( {135^\circ + 360^\circ } \right)}}{{\cos \left( {30^\circ + 5.360^\circ } \right) + \cos \left( {60^\circ + 10.360^\circ } \right)}}\\
= \frac{{\sin 45^\circ + \sin 135^\circ }}{{\cos 30^\circ + \cos 60^\circ }}\\
= \frac{{\frac{{\sqrt 2 }}{2} + \frac{{\sqrt 2 }}{2}}}{{\frac{{\sqrt 3 }}{2} + \frac{1}{2}}} = \frac{{2\sqrt 2 }}{{\sqrt 3 + 1}}\\
b,\\
B = \frac{{1 + \cos 1800^\circ .\tan \left( { - 390^\circ } \right)}}{{\tan \left( { - 420^\circ } \right)}}\\
= \frac{{1 + \cos \left( {5.360^\circ } \right).\tan \left( { - 30^\circ - 360^\circ } \right)}}{{\tan \left( { - 60^\circ - 360^\circ } \right)}}\\
= \frac{{1 + \cos 0^\circ .\tan \left( { - 30^\circ } \right)}}{{\tan \left( { - 60^\circ } \right)}}\\
= \frac{{1 - \cos 0^\circ .tan30^\circ }}{{ - \tan 60^\circ }}\\
= \frac{{1 - 1.\frac{{\sqrt 3 }}{3}}}{{ - \sqrt 3 }} = \frac{{3 - \sqrt 3 }}{{ - 3\sqrt 3 }}\\
c,\\
\cos x = - \cos \left( {180^\circ - x} \right)\\
D = \cos 0^\circ + \cos 20^\circ + \cos 40^\circ + ...... + \cos 160^\circ + \cos 180^\circ \\
= \left( {\cos 0^\circ + \cos 180^\circ } \right) + \left( {\cos 20^\circ + \cos 160^\circ } \right) + ...... + \left( {\cos 80^\circ + \cos 100^\circ } \right)\\
= 0 + 0 + 0.... + 0\\
= 0\\
d,\\
\tan x.\tan \left( {90^\circ - x} \right) = \frac{{\sin x}}{{\cos x}}.\frac{{\sin \left( {90^\circ - x} \right)}}{{\cos \left( {90^\circ - x} \right)}} = \frac{{\sin x}}{{\cos x}}.\frac{{\cos x}}{{\sin x}} = 1\\
E = \tan 5^\circ .tan10^\circ .\tan 15^\circ ......\tan 80^\circ .\tan 85^\circ \\
= \left( {\tan 5^\circ .\tan 85^\circ } \right).\left( {\tan 10^\circ .\tan 80^\circ } \right).....\left( {\tan 40^\circ .\tan 50^\circ } \right).\tan 45^\circ \\
= 1.1.1.....1\\
= 1\\
e,\\
co{s^2}x + {\cos ^2}\left( {90^\circ - x} \right) = {\cos ^2}x + {\sin ^2}x = 1\\
F = {\cos ^2}{15^2} + {\cos ^2}35^\circ + {\cos ^2}55^\circ + {\cos ^2}75^\circ \\
= \left( {{{\cos }^2}15^\circ + {{\cos }^2}75^\circ } \right) + \left( {{{\cos }^2}35^\circ + {{\cos }^2}55^\circ } \right)\\
= 1 + 1 = 2
\end{array}\)
