1) Prove the following: [tan (x) + 1]|cos*(x) – 1] = -tan²(x) %3D

Q: Find the periodic function f(x) = sinx + tan-+ sin- X + 23 + sin 2n+1 + tan ... 2n

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Q: 14. Find the smallest positive root of tan x+2 tanh x = 0.

A: Newton Raphson Method:- The root is xi+1 =xi - fxif'xi; i=0, 1, 2, ....   Given equation is tanx +2…

Q: 1//2 x8 Evaluate: sin" (1-2x')+ cos" (2axvi-x")} dx. 2x²)+cos* 1-x4 -1/V2

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Q: 1 - cos(3x) lim 3x х> 0 1 + Зх — е e

A: We , have                Given      lim 1-cos3x1+3x-e3x     x70We have to evaluate the…

Q: In cos 2x 4. Find lim x→0 In cos 3x

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Q: 1- r + In (x) lim 41 1+ cos (3a x)

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Q: Find sin 2x, cos 2x, and tan 2x if tanx= and x terminates in guadrant III. 3

A: To find the value of sin (2 x), cos (2 x), and tan (2 x).

Q: 1) Verify the power reducing formula, cos-x= 0:1 holds true for x = and x= =.

A: Here I am attaching image so that you understand each and every step.

Q: In(cos ax) ? limx-0 In(cos bx)

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Q: B: 3:Use Gamma & Beta properties to evaluate : f (In x) 3 dx

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Q: 36. (a) Prove the reduction formula 1 cos"-'x sin x + п S cos"x dx = | cos"-2x dx n n (b) Use part…

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Q: What values of x in the interval [0,2pi] satisfy 2 + 2cos(x) - sin2 (x) = 0

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Q: x2 – 1 - if x <1 x – 1 - f(x) = T In x a cos 2rx + b sin(- 4 In 2 if 1<x < 4 if 4 < x where a and b…

A: Explanation of the answer is as follows

Q: Determine a root of f(x) = 2* +3 cos(x²)-2 with 10-3 accuracy.

A: Given :f(x)=2x+3cosx2-2

Q: th The n derivatives of sin'x is 4" cos(4x + 8 2 thi

A: False

Q: Locate and identify the absolute extreme values of cos (ln x) on [1/ 2, 2].

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Q: -1 1- x² 1+x? Differentiate cos with respect to tan -1 2x 1- x2 '

A: Derivative of one function with respect to another function. Using substitutions to find derivative.

Q: Assuming In = [ cos" xdx. and n > 2: 1 п -1 n-1 r sin x + -In-2; CoS' In n %3D n

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Q: 1) VERIFY THE POWER REDUCING FORMULA, cos"x : cos 2x+1 HOLDS TRUE FOR 2 x = - AND x =

A: To verify:   cos2x=cos2x+12, for x=π3 and x=π2   NOTE: As per our answering guidelines, we can only…

Q: 4 Find sin 2x, cos 2x, and tan 2x if tanx and x terminates in quadrant IV. 3 sin 2.x cos 2.x tan 2.x…

A: Given:- tan(x) =-4/3 To find:- value of sin(2x), cos(2x), tan(2x)

Q: 4加 T (In cos x) Beca Cos X

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Q: 4. Derive error-bound formulas for the following expressions. i) cos(x) – sin(x) ii) In(x) + sin-1 y…

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Q: 15) lim cos (2x)

A: Let fx=cos2x

Q: Let tan A = 12/5 with A in Q1. Find exact value for cos(2A)

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Q: - 3in 2 X sin X- COSX

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Q: 1 os( 1 (sin(7z))* =| x)+ cos( x)

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Q: b. Express tanh x in terms of e* and e-* and hence show that 2 tanh x tanh 2x = 1+ tanh? x' c. Given…

A: (b) To proof :   tanh2x=2tanhx1+tanh2x It is known that, sinhx=ex-e-x2coshx=ex+e-x2 so,…

Q: 05. lim, (e* - 1)cos x

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Q: 14. Evaluate cos 3x+ dx. 2

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Q: 15 Suppose that tan a = TC <a<t. 2 and - Find the exact values of cos and tan 2 - JT Cos Undefined…

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Q: 7 sin(x) -dx 2 cos x+5cos(x)– 3 4.

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Q: 8 and x terminates in guadrant IV. 15 Find sin 2x, cos 2x, and tan 2x if tanx %3D

A: Given  tanx=-815,  x in quadrant IV

Q: Find all values of x in the interval [0, 2π] that satisfy the equation.   2 cos x - 1 = 0

A: From the given problem: 2cosx-1=0 Now solve: 2cosx-1=02cosx=1cosx=12cosx=cosπ3

Q: - (2D³ – D² + 1) (In cos x – 2 tan x)

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Q: 15 Find sin 2x, cos 2x, and tan 2x if cos.xr= and x terminates in quadrant IV. 17 sin 2x cos 2x !!…

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Q: 4 Find sin 2x, cos 2x, and tan 2x if cosx= and x terminates in guadrant III.

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Q: 1. Show that | sin x cos3 x dx = sin® x sin x +C = - 8. cos*x, cosx cosx +C 3

A: To prove:-

Q: a. Solve for real x, in the equation sinh 2x – 2 cosh 2x +2 = 0. b. Express tanh x in terms of e*…

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Q: 2 tan(2x) − 4 cos(x) = 0

A: Explanation of the solution is given below.... And solve the given equation.....

Q: For cos2(xy) = - evalu COS 4

A: Given

Q: 4. Prove that the identity is true. 1- cost e = sin² 0 1+ cos e

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Q: 3 Find sin 2.x, cos 2.x, and tan 2x if tanx and x terminates in guadrant II. 2 sin 2x %3D cos 2x tan…

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Q: = 2. If y = sin³ (-) cos³ (1) prove that y' = sin² (x) cos(x)

A: Topic = Derivative

Q: Where does the periodic function ƒ(x) = 2e^(sin (x/2)) take on its extreme values and what are these…

A: Given,

Q: In x 6- find lim + 3 + /3x dx 2 Jx 7- find 4 x, +x?)– Inx² -e In 99 dx | In(x 8- find (x+1) In°…

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Q: 1. Determine the smallest positive root of f(x) = Sin x + Cos ( 1+ x ) - 1. Use 5 %3D iterations of…

A: Given function is f(x)=sinx+cos(1+x2)-1 the graph of the function is From the graph we can see that…

Q: Find sin(2x), cos(2x), and tan(2x) from the given information. tan(x) = - cos(x) > 0 3 sin(2x) =D…

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.