tan(9π/4+a)*tan(3π/4+a)=?已知sin(a+30)=12/13 且60<a<90 求sina 的值?

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tan(9π/4+a)*tan(3π/4+a)=?已知sin(a+30)=12/13且60<a<90求sina的值?tan(9π/4+a)*tan(3π/4+a)=?已知sin(a+30)=12/13

tan(9π/4+a)*tan(3π/4+a)=?已知sin(a+30)=12/13 且60<a<90 求sina 的值?
tan(9π/4+a)*tan(3π/4+a)=?已知sin(a+30)=12/13 且60<a<90 求sina 的值?

tan(9π/4+a)*tan(3π/4+a)=?已知sin(a+30)=12/13 且60<a<90 求sina 的值?
tan(9π/4+a)*tan(3π/4+a)
=tan(2π+π/4+a)*tan(π-π/4+a)
= tan(a+π/4)*tan(a-π/4)
=(1+tana)/(1-tana)*(1-tana)/(1+tana)
=1

sina=sin(a+30-30)=√3/2*sin(a+30)-1/2cos(a+30)
60<a<90
90<a+30<120
cos(a+30)=-5/13
√3/2*sin(a+30)-1/2cos(a+30)
=√3/2*12/13+1/2*5/13
=(12√3+5)/26
所以sina=(12√3+5)/26