Given (SiNx + cosx) / (SiNx cosx) = 3, find the value of TaNx, 2Sin? X + (SiNx cosx) 2

Given (SiNx + cosx) / (SiNx cosx) = 3, find the value of TaNx, 2Sin? X + (SiNx cosx) 2

(sinx+cosx)/(sinx-cosx)=3
sinx+cosx=3sinx-3cosx
sinx=2cosx
tanx=sinx/cosx=2
sinx=2cosx
The identity sin? X + cos? X = 1 is introduced
cos²x=1/5
sinxcosx=2cosxcosx=2cos²x=2/5
sin²x=1-1/5=4/5
The original formula = 2 × 4 / 5 + sin 2 x + cos 2 - 2 SiNx cosx
=8/5+1-4/5
=9/5

TaNx = 2 x ∈ (π, 3 π / 2), find the value of [sin (π - α) + 2Sin (3 π / 2 + α)] / cos (3 π - α) + 1]

[sin(π-α)+2sin(3π／2+α)]／[cos(3π-α)+1]=[sinα-2cosα]／[-cosα+1]=[sinα/cosα-2cosα/cosα]／[-cosα/cosα+1/cosα]=[tanα-2]／[-1+1/cosα]=[2-2]／[-1+1/cosα]=0／[-1+1/cosα]=0

Proof (tanxtan2x / tan2x TaNx) / (tan2x TaNx) + √ 3 (sin ^ 2x cos ^ 2x) = 2Sin (2x - π / 3)

tanxtan2x/(tan2x-tanx)=sinxsin2x/(sin2xcosx-sinxcos2x)=sinxsin2x/sin(2x-x)=sin2x(tanxtan2x/(tan2x-tanx))+√3[(sinx)^2-(cosx)^2]=sin2x-√3cos2x=2sin(2x-π/3)

If cos (π / 4-x) = - 4 / 5 5 π / 4 < x < 7 π / 4, find the value of (sin2x-2sin ^ 2x) / 1 + TaNx Evaluate known π / 2

Cos (π / 4-x) = - 4 / 5, (√ 2 / 2) (cosx + SiNx) = - 4 / 5
So cosx + SiNx = - 4 √ 2 / 5 -------- (1)
Cos (π / 4 + x) = sin (π / 2 - π / 4-x) = sin (π / 4-x) = - 3 / 5 (because 5 π / 4

If 2 / 2 of the fraction [x squared + 2x + M] is always meaningful when x takes any real number, then the value range of M?

That is, the denominator is not equal to 0
That is, there is no solution for x 2 + 2x + M = 0
The discriminant is less than 0
4-4m1

If the square of (x + m) is a real fraction, then it is meaningful?

No matter whether M takes any real number, the denominator is never zero
Denominator = x? + 2x + m opening up
If it is not equal to 0, it is always greater than 0
That is, there is no intersection with the X axis
So the discriminant is less than 0
(2)²-4m1

If the fraction x squared-2x-m is 1, no matter what value x takes, it is always meaningful to find the value range of M

x²-2x-m=x²-2x+1+(-m-1)=(x-1)²+(-m-1)
-m-1＞0
m＜-1

What's the meaning of the fraction x minus x

So the square of X is not equal to 16
X is not equal to plus or minus 4
So x is not equal to 4 or X is not equal to - 4

If the square of the fraction x minus 2x and the fraction of M is 5x, regardless of whether x takes any real number, what is the range of M

5x / (x ^ 2-2x + m) is meaningful, that is, x ^ 2-2x + m is not equal to 0, which is consistent with the discriminant = (- 2) ^ 2-4m = 4-4m1

The fraction 4x-5 / 2x ^ 2 + X-6 is obtained by adding two fractions M / x + 2 and N / 2x-3. Find the value of M and n

Because M / (x + 2) + n / (2x-3) = m (2x-3) / (x + 2) (2x-3) + n (x + 2) / (2) (2x-3) + n (x + 2) / (x + 2) (2x-3) = (2mx-3m) / (x + 2) (2x-3) + (NX + 2n) / (x + 2) (2x-3) = (2mx-3m + NX + 2n + 2n + 2n) / (x + 2) (2x-3) = [(2m + n) x + 2n-3m] / (x + 2) (2x-3), so 2m + n = 4,2n-3m = - 5, the solution is m = 13 / 7 / 7 / 7 / 7 / 7, M = 13 / 7 / 7, the solution is n = 2 / 7