High school math solution questions, trigonometric identity transformation problems! Urgent

First find it according to the universal formula: sin( )2 + cos( )2 = 1, sin( )2 = 1 - cos( )2 = 1 5 because is an acute angle, sin = 1 5

In the same way, cos = 1 10

Since and are both acute angles, the range of - is -2 2 , so only the sum of the two angles can be used, sin( = sin cos -cos sin

You can't use cos( = cos cos +sin sin ] to get sin( = -1 2, so -= - 4.

The second floor is not as detailed as I wrote, hehe.

1. Substituting a special value, such as 30°, that is, 6, can get sin 6=, 3 * 6=, exclude AB, and then substitute into the CD formula, you can exclude C, and the answer is D

2, sin105cos105=sin(60+45)cos(60+45)=[sin60cos45+cos60sin45] *cos60cos45 -sin60sin45]=sin 45[sin60+cos60][cos60-sin60]=sin 45[cos 60-sin 60]=1 2 [1 4 -3 4]= -1 4 Answer B

3,sin(2x)tanx=2sinxcosx sinx cosx=2sin x,tan 2 does not exist, x≠ 2+k, then the simplified value range is no maximum, there is a minimum value of 0, and the answer is a

4. According to the formula cos(2 )=2(cos) 1, simplify the formula to obtain 1 2 *cos2x, then the period is , and the answer is d

5, tan( -=(tan -tan ) (1+tan ·tan), according to the formula, + 4) = + 4, replace 2 5 with, 1 4 with, you can get, (answer c

6. According to the formula cos(2)=2(cos) 1, tan(2)=(1-cos) sin, cot(2)=(1+cos) sin, sin(2)=2sin ·cos, after simplification, -sin cos = -1 2 sin2, the answer is a

7. According to the formula cos(2 )=2(cos) 1, you can put 2+2cos8=2+2(2cos 4-1)=4cos 4,1-sin8=1-2sin4cos4=(sin4-cos4), then the original formula can be simplified, because sin4 cos4 0, then the final simplification can be obtained.

2 (cos4-sin4)-2cos4=-2sin4 answer c

8, becomes 2 (1 2 sin 12 - 3 2 cos 12) = 2 sin ( 12 - 3) = 2 sin ( - 4) = - 2 answer choose b

The answers are dbadcacb

Do it == just the answer?

1d special value method takes x=6

105 degrees split into 45+60

3.A is cut into a string and the result is 2sinx 2, but tan2 is meaningless, so the maximum value cannot be taken.

Simplified to cos2x 2

The answer seems to be wrong, and it should be root number 3

f(x)=sin(2x- 3), because x [0, ] so 2x- 3 [- 3,5 3], so the image of the function f(x)=sin(2x- 3) is in [- 3,5 3], f(x)=m has two unequal real roots, combined with the image, we can know:

m∈(-1，-√3/2)u(-√3/2，1)。

You seem to have made a mistake in simplifying, fx=-sin(2x- 3), draw the image and you will find that the value range of m is (-1, root number 3 2).

To find the sum of two real roots, you can take the intersection point with the x-axis, because the sum of them does not change no matter how you move them.

The key to this kind of problem is to be proficient in the general skills of trigonometric transformations, and it is important not to forget to draw images.

The square of both sides of the second formula is added to the square of the two sides of the first formula.

2+cos(a-b)=13/36

So cos(a-b)=-59 36

Square the two formulas on both sides, and then use the first formula after the square to add the second formula, and get the first answer you ask for.

The second question is OK to use the sum and difference product of the positive Xuanding, so Bai is to use a sina=b sinb=c sinc=2r, bring it in, and use the square du difference formula.

zhi then uses the sum difference product to go up and down at the same time, and dao is about to reduce a sin(a+b).

In the third problem, we also use the positive metaphysical theorem to substitute the variables first, and then use the sum difference product of the right side and the upper body to get (sin(a+b)) 2sin(a-b), and then use the sum difference product to get (sin(a+b)) 2=(sin(a+b)) 2 by removing sin(a-b) on both sides, and then use -c=a+b to substitute the variables, we can get (sina) 2+(sinb) 2=(sin(c)) 2. That's a 2 + b 2 = c 2

The fourth problem is to do the formula operation first, add 2a 2b 2 on both sides at the same time to make a 4+b 4 into (a 2+b 2) 2, and then move 2c (a +b ) to the left side of the equation to continue the formula, and finally make it as: (a 2+b 2-c 2) 2=2a 2b 2, and then use the cosine theorem to replace a 2+b 2 with a 2+b 2.

c 2 + 2abcosc, you can calculate cosc=, that is, c is 45 degrees of the first question you wrote I can't understand...