已知α第二象限的角,f(a)=sin(a+π/2)cos(3π/2-a)tan(2π-a)除以tan(-a-3π）sin(-a-2π）求f(π/4）

题目

已知α第二象限的角,f(a)=sin(a+π/2)cos(3π/2-a)tan(2π-a)除以tan(-a-3π）sin(-a-2π）求f(π/4）

答案

f(a)=sin(a+π/2)cos(3π/2-a)tan(2π-a)÷{tan(-a-3π）sin(-a-2π)}
=cosa(-sina)(-tana)÷{[-tan(a+3π)][-sin(a+2π)]}
=cosasinatana÷{[-tan(a+π)][-sina]}
=cosasinatana÷{tan(a+π)sina}
=cosasinatana÷{tanasina}
=cosa
f(π/4)
=cosπ/4
=√2/2