Plural proof, It is proved that cos (z1 + Z2) = cosz1 * cosz2-sinz1 * sinz2

Using Euler formula
cos z=[e^z+e^[-z]]/2,sin z=[e^z-e^[-z]]/2i
You can replace the trigonometric functions on the left and right sides of the formula to be proved with the above formula

RELATED INFORMATIONS

1. Solving a complex geometry problem Given three complex numbers Z1, Z2 and Z3, if Z1 ^ 2 + Z2 ^ 2 + Z3 ^ 2-z1z2-z1z3-z2z3 = 0, it is proved that the triangle with Z1, Z2 and Z3 as vertices is regular triangle
2. If the point of complex number (a + I) 2 in the complex plane is on the negative half axis of Y axis, then the value of real number a is () A. 1B. -1C. 2D. -2
3. The complex number Z = M2-1 + (m2-m-2) I is: (1) real number; (2) imaginary number; (3) pure imaginary number
4. Z1 = x + y + (x ^ 2-xy-2y) I, Z2 = (2x-y) - (y-xy) I, ask when x and y are real numbers (1) Are Z1 and Z2 real numbers? (2) Z1 and Z2 are conjugate complex numbers?
5. 1: It is known that the equation x ^ 2 + (K + 2I) x + 2 + ki = 0 has a real root. Find the real root and the value of the real number K 2: Let Z be an imaginary number, ω = Z + 1 / Z be a real number, and - 1
6. Finding the third derivative of y = cos (INX)
7. Second derivative y = cos ^ 2x. INX + e ^ (- x ^ 2)
8. Finding the derivative of F (x) = [cos (INX)] ^ 2
9. Function y = sin (INX) + cos (INX) =?
10. Z = x ^ 2 + y ^ 2, and x = 1 + Sint, y = cost, find DZ / dt
11. Let a and B belong to n-dimensional matrices over complex field, a and B are commutative, that is, ab = ba. It is proved that the eigensubspace of a must be the invariant subspace of B
12. How to prove that a real matrix is similar to an upper triangular matrix over a complex field, and give a proof (not Jordan matrix)
13. Is fish plural?
14. Is fish plural? Besides fish on the table, is fish plural? Can you say: "there are many fishes in my home"? People on the third floor, but sheet also has a plural. The plural of sheet is itself
15. On the complex number of fish I remember n years ago when fish was said to be an uncountable noun, isn't that right? It should be a singular plural word, right? But what I doubt is that there is a problem .There __ fish in the lake . The answer is is, I am very confused, and there is another question in the book. What's your opinion? I hope the answer is wrong
16. Fish plural
17. Fish plural
18. Let the complex Z satisfy ZZ - + (2-I) Z + (2 + I) Z - + 4 = 0, and prove the distance from the point corresponding to Z on the complex plane to the point corresponding to complex - 2-I on the complex plane constant Z - is the conjugate complex number of Z, which is convenient to type
19. In the complex plane, the distance from the point corresponding to the complex number 1 + 2I to the origin
20. The distance from the corresponding point of complex number 1 + 1I in the complex plane to the origin is () A. 12B. 22C. 1D. 2