Known (tanx+1) / (2tanx+3) =2/7, find 1/ (2sinxcosx+cos^2x+1)

Known (tanx+1) / (2tanx+3) =2/7, find 1/ (2sinxcosx+cos^2x+1)

The original problem is: known (TaNx + 1) / (2tanx + 3) = 2 / 7, find 1 / (2sinxcosx + (cosx) ^ 2 + 1) from (TaNx + 1) / (2tanx + 3) = 2 / 7, a = TaNx = - 1 / 31 / (2sinxcosx + (cosx) ^ 2 + 1) = ((cosx) ^ 2 + (SiNx) ^ 2) / (2 (cosx) ^ 2) = (1 + A ^ 2) / (2 + 2A + A ^ 2)

Given that X and B belong to (0, π / 4,) TaNx / 2 divided by the square of 1-tanx / 2 = 1 / 4, and 3sinb = sin (2x + b), then the value of X + B?

By the condition, TaNx / 2 divided by the square of 1-tanx / 2 = 1 / 4, we get TaNx = 1 / 2. First, we multiply the two sides by 2. Then we use the formula instead because 3sinb = sin (2x + b), that is, 3sin [(x + b) - x] = sin [(x + b) + x], simplify, get 2Sin (x + b) cosx = 4cos (x + b) SiNx, get Tan (x + b) = 2tanx = 1, because x, B belong to (0, π / 4,), so x + B

tanx=2,sin²x+sinxcosx-2cos²=?

tanx=2,sin²x+sinxcosx-2cos²=(sin²x+sinxcosx-2cos²)/(sin²x+cos²)
=(tan^2x+tanx-2)/(tan^2x+1)
=(4+2-2)/(4+1)=4/5

The square of sin (x + 15 degrees) - the square of sin (X-15 degrees) = 1 / 4. Find TaNx X is between 45 and 90 degrees

sin²(x+15°)-sin²（x-15°）=【sin(x+15°）-sin(x+15°）】【sin(x+15°）+sin(x+15°）】=（sinxcos15°+cosxsin15°+sinxcos15°-cosxsin15°）（sinxcos15°+cosxsin15°-sinxcos15°+cosxsin15°）=...

If sin (π / 4 + x) = 5 / 13 and X ∈ (π / 4,3 π / 4), then (1-tanx) / (1 + TaNx)=

sin(π/4+x)=5/13
cos(π/4+x)=-12/13
sinx=sin(π/4+x-π/4)
=sin(π/4+x)cos(π/4)-cos(π/4+x)sin(π/4)
=5/13*√2/2+12/13*√2/2
=17√2/26
cosx=-7√2/26
tanx=-17/7
(1-tanx)/(1+tanx)=-12/5

Sin (x + π) is known 4)＝3 5，sin(x− π  4)＝4 5, then TaNx=______ .

∵sin(x+ π 
4)＝3
5，sin(x− π 
4)＝4
5，
Qi
Two
2(sin⁡x+cos⁡x)＝3
Five
Two
2(sin⁡x−cos⁡x)＝4
5 ，
Comparing the two formulas, sin ⁡ x + cos ⁡ x is obtained
sin⁡x−cos⁡x＝3
4，
That is 4sinx + 4cosx = 3sinx-3cosx,
∴sinx=-7cosx，
∴tanx=-7，
So the answer is: - 7

X + 5 divided by X squared + 1 under what conditions does this fraction make sense

X 2 + 1 is greater than 0 for any real number
ν x is any real number

Is one part of x+y a fraction? What is the definition of fraction? The sum of X and Y is a bit fraction, not the reciprocal of the sum of X + y is a bit fraction,

Definition: integral a divided by integral B can be expressed as a / B. If Division B contains letters, then it is called fraction. Note: a △ B = a × 1 / BII. Composition: in fraction, a is called the numerator of fraction, and B is the denominator of fraction

When x =? 1 / 1 of fraction (1-x) is meaningless

Because it's meaningless
therefore
（1）
Denominator = 0
1-1/x=0
X=1
（2）
When x = 0
1 / X meaningless
So 1-1 / X is meaningless
Zongshang
It is meaningless when x = 1 or 0

When x is taken, the fraction x ^ 2-x-2 x + 3 is meaningless

x^2-x-2=0
(x-2)(x+1)=0
x1=2 x2=-1
When x equals - 1 or 2, the fraction is meaningless