wyznacz liczbę - trygonomeria

dsz_nk89 · Post autor: **dsz_nk89** » 8 kwie 2017, o 07:46

Wyznacz liczbę \(\displaystyle{ a= \frac{\cos ^{2}43 ^\circ - \cos ^{2}47 ^\circ}{11 \sin 2 ^\circ\cos 2 ^\circ}}\)

kerajs · Post autor: **kerajs** » 8 kwie 2017, o 09:02

\(\displaystyle{ a= \frac{\cos ^{2}43 ^{\circ } - \cos ^{2}47 ^{\circ }}{11 \sin 2 ^{\circ }\cos 2 ^{\circ }}=
\frac{\left( \cos 43 ^{\circ } +\cos 47 ^{\circ }\right) \left( \cos 43 ^{\circ } - \cos 47 ^{\circ }\right) }{11 \sin 2 ^{\circ }\cos 2 ^{\circ }}= \\
= \frac{\left( \cos (45 ^{\circ }-2 ^{\circ }) + \cos (45 ^{\circ }+2 ^{\circ })\right) \left( \cos (45 ^{\circ }-2 ^{\circ }) - \cos (45 ^{\circ }+2 ^{\circ })\right) }{11 \sin 2 ^{\circ }\cos 2 ^{\circ }}=\\
....\\....\\= \frac{2}{11}}\)