If sin2x cos x a 0 has a real root, try to determine the range of the value of the real number a

It's so simple, whoever loves to do it does it.

Problem: Containing Tanruo sinx=(a+2) (a-2), find the value range of the real number a From the question, sinx=(a+2) (a-2) Because the value range of Mengtong sinx is [-1,1], we know that the value range of Liang Yi (a+2) (a-2) is [-1,1] and the value range of solving a is [0,3 2].

Because -1 sinx 1

So -1 a+2 1

3≤a≤-1

Therefore, the value range of the real number a is [-3, -1].

Knowing that Saiyin x is equal to a plus 2, ask what is the range of values of the real number a, Saiying x is the Sincosine function, and its value has a range from -1 to positive, so that is, a plus 2 is greater than or equal to -1 less than or equal to justice, and move two to both sides of the symbol, that is, a is greater than or equal to -3 less than or equal to -1

Convert the original equation to: a=-sin2x-cosx=cos2x-cosx-1, let cosx=t,t [-1,1], then a=t2-t-1=(t-1

So the answer is: [-5

The separation parameter is an important mathematical idea, that is, a=-sin x-cosx=-(1-cos x)-cosx=cos x--cosx-1=(cosx-1 2) -5 4, since the value range of cosx is [-1,1], the value range of the real number a is [-5 4,1].

sin²x+cosx+a=0 ＝》1-cos²x+cosx+a=0 #

Another t=cosx, then the formula is 1-t +t+a=0 > t -t-(a+1)=0 *

If there is a solution to the equation, then greater than or equal to zero solution to this inequality...

Triangles can't be typed... I'll see it below).

sinx-cos2x sinx-(1-sinx 2)=2sinx 2+sinx-1, let y=sinx, then the value range of y is [-1,1], so 2sinx 2+sinx-1 2y 2+y-1,y [-1,1].

When y=-1 4, 2y 2+y-1 has a minimum value, i.e., 2*(-1 4) 2+(-1 4)-1=-9 8

Therefore, the value range of a is a<-9 8

1-2(1-sin²x)-sinx+a=0a=-2sin²x+sinx+1

2(sinx-1/4)²+15/8

1<=sinx<=1

So sinx = 1 4 and a max = 15 8

sinx = -1, a minimum = -2

So -2< = a< = 15 8

cos2x+2sinx+a=1-2sin 2 x+2sinx+a=0, so 2sin 2 x-2sinx-1-a=0, so sinx=t, then 2t 2-2t-1-a=0, the discriminant formula of this function is 4+8(1+a)>=0, i.e., a>=-3 2