cos(2arctan√2+π/3)的值为

cos(2arctan√2+π/3)的值为
cos(2arctan√2+π/3)的值为

cos(2arctan√2+π/3)的值为
令a=arctan√2
则tana=√2
则sina/cosa=√2
sina=√2cosa
sin²a=2cos²a
代入sin²a+cos²a=1
cos²a=1/3,sin²a=2/3
所以cos2a=cos²a-sin²a=-1/3
sin2a=2sinacosa=2(√2cosa)cosa=2√2cos²a=2√2/3
所以原式=cos2acosπ/3-sin2asinπ/3
=(-1-2√6)/6