设a属于(π/2,3π/4),sin2a=n,则sina+cosa=?

Question

设a属于(π/2,3π/4),sin2a=n,则sina+cosa=?

Answer 1

a属于(π/2,3π/4) sina>0 cosa|cosa|（由函数图象可知)
所以sina+cosa>0
(sina+cosa)^2=1+2sinacosa=1+sin2a=1+n
所以sina+cosa=√(1+n)