Why is the x power of E plus the negative x power of e equal to the 2x power of E plus one

How is that possible?
Is it (e ^ x + e ^ - x) / (e ^ x-e ^ - x)?
In this way, the upper and lower parts are multiplied by e ^ X
Get (e ^ 2x + 1) / (e ^ 2x-1)

Simplification: (SiNx) ^ 4 + (cosx) ^ 2 - (SiNx) ^ 2

=(sinx)^4+1-2(sinx)^2=[(sinx)^2-1]^2=(cosx)^4

Simplification: [1 - (SiNx) ^ 4 - (cosx) ^ 4] / [(SiNx) ^ 2 - (SiNx) ^ 4]

Molecule = 1 - (COS ^ 4x + sin ^ 4x)
=1-[(sin²x+cos²x)²-2sin²xcos²x]
=2sin²xcos²x
Denominator = Sin & sup2; X (1-sin & sup2; x)
=sin²xcos²x
So the original formula = 2

RELATED INFORMATIONS

1. How to simplify SiNx ^ 4 + cosx ^ 4, What about SiNx ^ 4-cosx ^ 4
2. Find the maximum and minimum values of the function f (x) = [(SiNx) ^ 4 + (cosx) ^ 4 + (sinxcosx) ^ 2] / (2-2sin2x), and point out the value of X when the maximum value is taken?
3. What is higher order infinitesimal? How to apply it in finding limit? Give an example
4. Let's ask a limit problem. If a (x) is an infinitesimal of higher order of X, then when x approaches zero, a (x) / x = 0, and a (x) * x / x = 0, right?
5. Sum of infinitesimals and sum of infinitesimals The sum of infinitesimals is not necessarily infinitesimal. It may be infinitesimal, infinitesimal or bounded However, the sum of finite infinitesimals is infinitesimal. I am a little confused about these two problems. Can you give me a simple example to explain them?
6. Try to determine the values of constants a, B and C such that e ^ x * (1 + BX + CX ^ 2) = 1 + ax + ο (x ^ 3), where ο (x ^ 3) is the infinitesimal of higher order than x ^ 3 when x → 0 There is an answer (e^x)*(1+Bx+Cx^2)=(1+x+x^2/2!+x^3/3!+o(x^3))*(1+Bx+Cx^2)=1+(1+B)x+(1/2+B+C)x^2+(1/6+B/2+C)x^3+o(x^3)=1+Ax+ο(x^3) So, there are 1 + B = a, 1 / 2 + B + C = 0, 1 / 6 + B / 2 + C = 0 The solution is: a = 1 / 3, B = - 2 / 3, C = 1 / 6 But I can't understand the second equal sign
7. When x tends to zero, which is higher order infinitesimal compared with SiNx (TaNx + x ^ 2)
8. Taking x as the base infinitesimal, finding the principal part of (x + SiNx ^ 2) ^ 3 Is [x + sin (x ^ 2)] ^ 3 There is another: sin (x + π / 6) - 1 / 2 is still principal
9. If the function f (x) is defined near x = 0, and f (0) = 0, f ′ (0) = 1, then limx → 0f (x) x = 1
10. Finding the limit process of (sin2x-1) / X when the limit x tends to 0 Find the limit of (sin2x-1) / X when x tends to 0 process
11. lim[ln(1+x)+ln(1-x)]/(tanx)^2
12. Find the limit X - > 0 + (1-cosx) (x ^ x-1) ((√ x + 1) - 1) / (1 + cosx) ^ 2 * LNX * arctan (x ^ 2) ^ 2
13. Commonly used equivalent infinitesimal x ^ 4-2x ^ 2 ~ - 2x ^ 2, which I can't understand at all X tends to zero
14. It is proved that limx → ax ^ 5 = ax ^ 5 limit holds by the definition of function limit lim x^5=a^5 x→a That's right: | x ^ 5-a ^ 5| How to prove x ^ 5 = a ^ 5
15. Find the monotone interval and extremum of the cubic power of y = x minus three X
16. What is the second power of X divided by the second power of X?
17. Find LIM (n → + ∞) (1 + n) [ln (1 + n) - ln n]
18. Find the solution set of (x + 2) > = 0 under the root sign of inequality (x-1) * and seek the help of God
19. (e ^ x ^ 2 + 2cosx-3) / x ^ 4 x tends to 0, and the limit is 7 / 12
20. Y = (x + 1) * ln (x + 1) / x, when x infinitely approaches 0, what is the limit of Y? The answer is 1. I want to deduce the process