Ai giúp e vs ạ rút gọn biểu thức : cos(a+2020π)-2sin(a-7π)-cos3π/2 – cos(a+2019π/2 ) + cos(a-3π/2).cot(a-8π) 05/10/2021 Bởi Hadley Ai giúp e vs ạ rút gọn biểu thức : cos(a+2020π)-2sin(a-7π)-cos3π/2 – cos(a+2019π/2 ) + cos(a-3π/2).cot(a-8π)
Giải thích các bước giải: Ta có: \(\begin{array}{l}\cos \left( {a + 2020\pi } \right) – 2\sin \left( {a – 7\pi } \right) – \cos \dfrac{{3\pi }}{2} – \cos \left( {a + \dfrac{{2019\pi }}{2}} \right) + \cos \left( {a – \dfrac{{3\pi }}{2}} \right).\cot \left( {a – 8\pi } \right)\\ = \cos \left( {a + 2.1010\pi } \right) – 2\sin \left[ {\left( {a – \pi } \right) – 3.2\pi } \right] – 0 – \cos \left[ {\left( {a – \dfrac{\pi }{2}} \right) + 2.505\pi } \right] + \sin \left[ {\dfrac{\pi }{2} – \left( {a – \dfrac{{3\pi }}{2}} \right)} \right].\cot \left( {a – 8\pi } \right)\\ = \cos a – 2\sin \left( {a – \pi } \right) – \cos \left( {a – \dfrac{\pi }{2}} \right) + \sin \left( {2\pi – a} \right).\cot a\\ = \cos a + 2\sin \left( {\pi – a} \right) – \cos \left( {\dfrac{\pi }{2} – a} \right) + \sin \left( { – a} \right).\dfrac{{\cos a}}{{\sin a}}\\ = \cos a + 2\sin a – \sin a – \sin a.\dfrac{{\cos a}}{{\sin a}}\\ = \cos a + 2\sin a – \sin a – \cos a\\ = \sin a\end{array}\) Bình luận
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\cos \left( {a + 2020\pi } \right) – 2\sin \left( {a – 7\pi } \right) – \cos \dfrac{{3\pi }}{2} – \cos \left( {a + \dfrac{{2019\pi }}{2}} \right) + \cos \left( {a – \dfrac{{3\pi }}{2}} \right).\cot \left( {a – 8\pi } \right)\\
= \cos \left( {a + 2.1010\pi } \right) – 2\sin \left[ {\left( {a – \pi } \right) – 3.2\pi } \right] – 0 – \cos \left[ {\left( {a – \dfrac{\pi }{2}} \right) + 2.505\pi } \right] + \sin \left[ {\dfrac{\pi }{2} – \left( {a – \dfrac{{3\pi }}{2}} \right)} \right].\cot \left( {a – 8\pi } \right)\\
= \cos a – 2\sin \left( {a – \pi } \right) – \cos \left( {a – \dfrac{\pi }{2}} \right) + \sin \left( {2\pi – a} \right).\cot a\\
= \cos a + 2\sin \left( {\pi – a} \right) – \cos \left( {\dfrac{\pi }{2} – a} \right) + \sin \left( { – a} \right).\dfrac{{\cos a}}{{\sin a}}\\
= \cos a + 2\sin a – \sin a – \sin a.\dfrac{{\cos a}}{{\sin a}}\\
= \cos a + 2\sin a – \sin a – \cos a\\
= \sin a
\end{array}\)
Bạn xem hình