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<>3 f( )sin( cos(2 cos( tan(

Then f( 31

3) is

Analysis: f( )sin cos

cos αtan α

cos α，f(－31π3)＝－cos(－31π3)＝－cos31π3

cos(10π＋π3)＝－cosπ3＝－1

Answer: 14 Let the function f(x) sin x cos x, f (x) be the derivative of f(x), if f(x) 2f (x), then sin2x sin 2xcos2x

Analysis: f(x) sin x cos x, f (x) cos x sin x, sin x cos x 2(cos x sin x), i.e. 3sin x cos x, get tan x 1

So sin2x sin 2xcos2x sin2

x－2sin xcos xcos2 x

tan2x－2tan x＝19－23＝－5

Answer: 5 3. Answer Question 5 The equation for x is known 2x2 (3 1) x m 0 of the two sins and cos ,0,2 ), find:

1)sin2θsin θ－cos θ＋cos θ

1 tan value; (2) the value of m;

3) The two roots of the equation and the value at this time

Solution: (1) Original sin2 sin cos cos

sin θcos θ

sin2θsin θ－cos θ＋cos2θcos θ－sin θ sin2θ－cos2θsin θ－cos θ

sin θ＋cos θ.By the condition known sin cos 3 1

Therefore, sin2 sin cos cos 1 tan

2) By sin2 2sin cos cos2 1 2sin cos sin cos )2, get m 3

3) by sin cos

sin θ·cos θ＝

4 Know, sin 3

2cos 12 or

sin θ＝12，cos θ＝3

and (0,2), so 6 or

Can you see it?

The computer can't see it at all, and asks that?

The first question is that as long as you know how to factor, you can calculate it according to the known conditions. The second question uses a common formula for inequalities, and the specific solution is shown in the figure below.

Move the root sign 2x+y to the right of the equal sign, both sides are squared, and all the quadratic terms at the end should be eliminated by m, so as to find the range of values of m.

Let p(m,n),q(s,t), then: vector ap=(m-2,n-1), vector pb=(4-m,-3-n).

1) Substituting =1 to get the binary system of equations: m-2=4-m, n-1=-3-n

Solution: m=3, n=-1 [if you are proficient, you can see that p is the midpoint of ab].

So: vector op = (3, -1), vector pq = (s-3, t+1).

The dot product of the two: 3(s-3)-(t+1)=0

Also note that q is on ob, so the vector oq is collinear with ob: s 4=t (-3).

Combining the above two equations yields: s=8 3, t=-2, i.e., q coordinates (8 3, -2).

2) Vector ap=(m-2,n-1)= · vector pb= (4-m,-3-n).

Same understanding: m=(4 +2) ( +1), n=(1-3 ) ( +1) [note ≠-1].

Remember the angle between the vector op and om, according to the geometric meaning of the vector dot product: op·om=|op||om|cosθ

When is an acute angle, cos >0, consider |op||om|Non-negative, so op·om>0

Substituting the coordinates of the vector to get the inequality:

Solution: >1 or <-4 3

1)an^2-(2n-1)an-an=0;

an-2n)(an+1)=0;

Because an>0;

Therefore, mu is prepared an=2n;

2) bn=1 (n+1)an=1 argue lead (n+1)2n=1 2*[1 n-1 (n+1)], and then sum it yourself.

The result is tn=1 2*[1-1 with good resistance(n+1)]=n 2(n+1).

If there is anything you don't understand, you can ask at any time, I will try my best to answer, I wish you academic progress, thank you.

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