用三角换元法证明不等式是基本方法,根据题意恰当地进行换元,则可使问题快速获解,达到事半功倍的效果.例1设点P(x,y)是圆x~2+(y-1)~2= 1上任意一点,若总有x+y+c≥0,试求c的取值范围.解因为点P(x,y)在圆x~2+(y-1)~2= 1上,故可设x=cosθ,y=1+sinθ,则x+y+c=cosθ+sinθ+1+c≥0恒成立, The use of triangular substitution method to prove inequality is the basic method. According to the problem, the problem can be solved quickly and achieve a multiplier effect. Example 1 Let the point P(x,y) be circle x~2+( Y-1) ~ 2 = 1 at any point, if there is always x + y + c ≥ 0, try to find the range of c. Solution because the point P (x, y) in the circle x ~ 2 (y-1 ) ~ 2 = 1, so we can set x = cos θ, y = 1 + sin θ, then x + y + c = cos θ + sin θ +1 + c ≥ 0 constant hold,