3. Show that cos 30 = cos 0 – 3 cos 0. [Hint: Apply De Moivre's Theorem.] |

Q: Example5:- Solve "-2¹-3y=³e5cos(31) 3

A:

Q: Solve:(1/x + 2) =[(4/x2 - 4 )- (1/x - 2)]

A: We need to take LCM and then to solve the equation.

Q: Does the symbol for infinity (q) represent a real number?

A: Yes, the symbol for infinity (∞) represents a real number.  Infinity (∞) means a very big number.…

Q: Solve the equation for positive integer n: ()-() (4,

A: Given that:n9=n4n!9!(n-9)!=n!4!(n-4)!9!(n-9)!=4!(n-4)!

Q: Express x = 31-!, y = 8t-2 in the form y = f(x). (Express numbers in exact form. Use symbolic…

A:

Q: Simplify : [(2 - 6/(x + 1).( 1 + 3 / (x - 2)]

A:

Q: tan

A:

Q: -4) 12x+30= 3xー12

A: we first distribute the equation, Then combine like term on same side.

Q: 1 + 1 + 1 + 1 + 1 1+1+1+1+1 1 + 1 x 0 + 1 = ?

A: Given: 1 + 1 + 1 + 1 + 1 1 + 1 + 1 + 1 + 1 1 + 1 x 0 + 1 = ?

Q: (4/5 - s)2/3 +1) b)

A:

Q: Evaluate ∑8 i=1 −3 × (−5)i−1

A:

Q: Solve: (tango)Ccos 6x) =-Sin33C 11

A:

Q: Is Vilr- 2)" =(x- 2)“, for x22 and a is a constant, what is the value of a ? а. 4 b. c. d. H

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Q: 4 -- ICI iC =(-1 4

A:

Q: use the equation y=x² - 17x + 72. For what values of x is yis greater than and equal to 0?

A: Given query is to find the values of x for which y is greater than equal to zero

Q: Conplex Fourien -2<メ<-ト -くx< 一<x<2 fox=

A:

Q: Cscx cotx dx 1+ 9csc²x

A:

Q: Solve the following equations using substitution: a) n-6vn+83D0 b) 2m^4-m^2-3=0 c)1/(m-2)-m/(m+3)%32

A: Here ix the solution

Q: If the roots of the equation a(b – c)x² + b(c – a)x + c (a – b)=0 2 1.1 are equal, show that b а с a

A: Here we will show that 2b=1a+1c

Q: Solve for real x the equation 9* + 6* = 4*

A:

Q: Choose the formula in which TWO instances of the variable "x" are free:  a) ((∀x)Gx -> (Fx -> Hx))…

A: In the given question we have to choose the correct option from the given options s.t two instance…

Q: (D) 1,x+27y= I.

A: The objective is to fill in the blank with appropriate answer.

Q: Solve equation: (AUX)B=AUBX

A: Given: A∪X×B=A∪B×X Now, A∪X×B=A×B∪X×B

Q: 2 3 -1 XX-2

A: Given query is to find the value of x.

Q: Solve

A: Give equation is

Q: (a) eln(8x) = 8. Answer: x = (b) 10log(8x+5) = 8. Answer: x =

A: Ln is to the base e and log is to the base 10

Q: If A 0 " P= [13] AP= PA, then what is A¹⁰ ?

A: Given: A=5-230, P=1213 To find: A10.

Q: fu)=5+5X6 find inverse

A: Here given function as fx=5+5x-6 ; x≥65

Q: Solve: x²y!" + 8ry + 6y = 0

A:

Q: find (1+2i)^5/3 write your final answer in a+bi form

A: We have to express in terms of a+bi.

Q: x2 - y² =2xy

A:

Q: Solve the exponential equations: A) e²x - 4ex - 5 = 0 B) 2x+¹= 3²x-1

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.