High School Mathematics If cos 4 x 4 5, 5 4 x 7 4, find the value of sin2 x 2sin x 1 tanx

cos( 4-x)=-4 5 gives sinx+cosx =-4 2 5 (1).

Synoptic sin x+cos x=1 to obtain 2sinxcosx=7 25 (2).

And because 5 4 x 7 4 , 0 cosx- sinx, so cosx- sinx=3 2 5 (3) simplify(sin2x-2sin x) 1+tanx =cosx (sin2x-2sin x) cosx+sinx

cosx(2sinxcosx-2sin x) cosx+sinx2sinxcosx(cosx-sinx) cosx+sinx substitute (1)(2)(3) to get the original formula =-21 100 I don't know if it's right, but the method should be correct.

Can it solve your problem?

Because cos( 4-x) = -4 5, cos( 4)cosx + sin( 4)sinx = -4 5

cosx+sinx=-4 5 change number 2. Because of the range of x, sinx is negative, and then the equation is solved.

The first one, using the commutation method, makes x=tan(u 2)

Question 2. 1/cos^3x=sec^3 (x).The same as the integrals of the first question for u.

Question 3, :

Solution: (1) Simplification first.

f(x)=sin(x+π/6)+sin(x-π/6)+cosx+a=sinxcosπ/6+sinπ/6cosx+sinxcosπ/6-sinπ/6cosx+cosx+a

3x sinx + cosx + a

2sin(x+π/6)+a

When sin(x+6)=1, f(x) is maximum, and the maximum value is 2+a 2+a=1

a=-12) from (1) to obtain f(x)=2sin(x+6)-1f(x)>=0, i.e., 2sin(x+ 6)-1>=0 sin(x+ 6)>=1 2

2k + 6<=x + 6<=2k +5 6 The solution yields (3) x [0, ]x+ 6 [ 6,7 6] The maximum value of f(x) is 1, and the minimum value is f( )=2sin(7 6)-1=-2

The value range is [-2,1].

Have fun! I hope it can help you, if you don't understand, please ask, I wish you progress! o(∩_o

Take the known conditions, calculate the value of cosx-sinx, square it, and get the value of 2sinxcosx. Then use the relationship between the square of cosx-sinx and the square difference of cosx+sinx by 4sinxcosx, calculate the value of cosx+sinx, pay attention to the value range of x at this time, and the value of cosx+sinx should be negative! Simplify the formula to be sought, tanx is written as sinx cosx, the denominator is divided, and the numerator extracts the common factor, and what you get is the formula about cosx-sinx, sinxcosx, cosx+sinx, and substitute the value just now to come out, hehe.

a=pie 4+x can be judged to be the fourth quadrant, so sina = -4 5

tana=-4/3 tan(2a)=24/7=-cot(2x)

Result = 2tan 2x(1+tanx) [(1-tanx)(1+tan 2x)] = tan(2x)*tan(pai 4+x) = -7 24*(-4 3) = 7 18

Can't see clearly, please go on**!