tan675°+cos675°-sin(-5π/2)+1/cos(-17π/3)
=tan(720°-45°)+cos(720°-45°)-sin(-5π/2+2π)+1/cos(-17π/3+6π)
=-tan45°+cos45°-sin(-π/2)+1/cos(π/3)
=-tan45°+cos45°+sin(π/2)+1/cos(π/3)
=-1+√2/2+1+1/(1/2)
=√2/2+2