Question

3sinx-2cosx=0 (1)(cosx-sinx)/(cosx+sinx)+(cosx+sinx)/(cosx-sinx) (2)sin^2 x-2sinxcosx+4cos^2 x

Answer 1

因为 3 sin x -2 cos x =0,
所以 sin x /2 =cos x /3.
令 sin x =2k, cos x =3k, k≠0.
(1) 原式= (3k -2k) /(3k +2k) +(3k +2k) /(3k -2k)
= (1/5) +5
= 26/5.
(2) 原式= (2k)^2 -2 (2k) (3k) -4 (3k)^2
= -44 (k^2).
又因为 1= (sin x)^2 +(cos x)^2
= (2k)^2 +(3k)^2,
所以 k^2 = 1/13.
所以 原式= -44/13.
= = = = = = = = =
以上计算可能有误.
如果给的条件是
tan x =2/3,
按同样方法做.