5) x. sec?x dx a) x tanx – In|cosx| + c c) tanx – In/cosx|+c b) x tanx + In|cosx| +c d) tanx + Injcosx|+c

Q: Give the degree of 0 = tan-(-V3) if it exists. measure %3D

A: topic - inverse trigonometric ratios

Q: 2: Prove that a) cosx tan3x = sinx tan’x b) (sin x + cos x)² = 1 + sin 2x

A:

Q: Prove that sec x dx = In sec x+ tan x +C.

A: Here the question is solving by using u-subsitution method.

Q: If y=tanx, Prove that Y™ 2 (Y²+1)(3+1)

A: We will find the required.

Q: (a) Buktikan, Prove that, (sin x + cos x)* = sin" 2x + 2 sin 2x + 1. %3D

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: tan 0 de equals to : 1+sece In |1+tane|+c In |1+sece|+c O (tane)^2/2+c -In |1+cose|+c

A:

Q: Prove that: 1) csc 0 + tan 0 . sec 0 csc 0.sce20 1-cos" x 2) sin x .cos x tan x 3) 3 cos' x-sia x+1…

A:

Q: tan u du = In | sec u| + C

A:

Q: a) Buktikan, Prove that, (sin x + cosx)* = sin 2x + 2 sin 2x +1.

A: The given equation,sinx+cosx4=sin22x+2 sin2x+1

Q: Where are the theta valuss for the horizontal and vertical tangent lines on [0,2pi) of r=1+cos theta

A:

Q: 6. By using u = tan 0, evaluate | tan 0 sec*e de .

A:

Q: Which of the following is equal to tan(T – 0)? sin(0) O cos(0) O sec(0) O csc(0) tan(8) cot(8) -…

A: Just I have used the trigonometrical formulas and identity and get the required solutions.Solutions…

Q: (cose+ tane) de / (sece + tan@sec2e) de cos e COS True (B) False

A: We have to find out

Q: Prove that d/dx tan(x) = sec^2(x).

A:

Q: (b)Prove that if f (x) = In (cosx), then f'(x) = -tanx.

A:

Q: Where does sin x have a horizontal tangent line? Where does cos xhave a value of zero? Explain the…

A: Concept: The function f(x) at the point x=a, is a line that just touches the graph of the function…

Q: Find tanget line to f(X) =tan(X) + 9 cos( X) at X=π

A:

Q: Prove the identity. cos (x+y) 1- tanx tany cosx cosy

A: We need to prove the following identity cosx+ycosx cosy = 1-tanx tany

Q: Show that x² + 1 cos{arctan[sin(arccot x)]} = V x² + 2

A:

Q: d Prove that sin x cos x from first %3D dx principles only. Be sure to prove any limits that are…

A: Let's learn first principle of derivative because we have to find derivative of sinx using first…

Q: If Y=tanx prove that %3D2

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Q: 8. Show that cos a – cos y| < |x – y| for all æ and y.

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Q: Find if r = sin[cos(-0)]. de dr = sin 0 cos(cos 0) de dr cos[sin(-0)] de Option 3 Option 1 dr dr sin…

A: This question is based on application of Derivative.

Q: 2. * 1 Add File 3. * 1 y = tan x + =tan³x 3 4. * y = = cos x 1 Add File y 1 cos³x 3 1 cosx

A:

Q: Set u = sec (8x) + tan(8 - x). • Step 1: ● ● ● du dx Step 2: = dx = Step 3: 8( sec (8x tan (8x)) +…

A: We need to find the given integral:       ∫sec28x+sec8x·tan8xsec8x+tan8x dx

Q: 46 a Show that cos x+ =-sinx. = -sinx. d" (cosx) = cosx + drn b Prove that

A:

Q: Show that (tan−1 x)'= cos2(tan−1 x) and then use Figure to prove that (tan−1 x)' = (x2 + 1) −1.

A: The objective is to show that:  tan-1x'=cos2tan-1x.   Use the formula: ddxf-1x=1f'f-1x. Here,…

Q: D,(6 tan x) 6 sec² x sec² x (c) D,(In |6 tan x|) %3D 6 tan x 6 tan x tan x

A: Consider the given function as Dxln6tanx

Q: Show that cos( arctan( sin( arccot(x)))) = sqrt{{x^2+1}/{x^2+2}}

A:

Q: Prove that sin (x +y) sin (x - y) tan x + tan y) %3D tan x – tan y

A:

Q: Compute tan" z · sec² æ dæ. O tan12 z tan10 z +C 12 10 O tan° a tan10 a +C 10 tan12 a sec æ +C 3 12…

A:

Q: (a) Show that tan x = dx sec?x using quotient rule.

A:

Q: Q4: Prove that: secx • cscx = tan x + cot x

A: According to guidelines we should have been able to solve only one question at a time #4

Q: the exprression csc x/sec x  is equivalent to: 1.  sin x 2. cos x 3. tan x 4. cot x

A: *to find:-  csc x/sec x = ?

Q: HW/ Prove that: (1) 1-tanif x sechx

A:

Q: prove that = - Cotx + C 1- cosx +Sin'x

A: According to the question, we need to evaluate the integration: F(x) = 2(1 - cos2x + sin2x) We need…

Q: (b) Can we use the IVT to conclude that f (x) = tan(x) equals 0 for some c in (0, 1)? %3D

A: We can answer first question among which you asked as per the honor policy. please resubmit the…

Q: Evaluate: | sech[In cosx]tanx dx A -2 tan -1(e cosx) +C В -2 tan -1(cosx) +C 2 tan -(ecosx) + C (D 2…

A:

Q: Given that | sec (x) dx = tan(x) + A and tan(x) dx = ln | sec(x)| + A. Show that O sec2(0) d0 = 0…

A:

Q: n x)(\sec x+\tan x) \equiv \cos x, \quad nathbb{Z} .

A: (a)  To prove that: (1-sinx)secx+tanx≡cosx

Q: Let w- fx.y.) - :), x- cos(), y sin(» and :. Then:

A:

Q: Show that tan(arccosx) for |x| s 1, x + 0.

A:

Q: Use Figure 7 to prove that (cos- x)': V1 x2 1 V1-x y FIGURE 7 Right triangle with y = cos- x. %3D

A: y=cos-1x⇒x=cosy

Q: Use the substitution u = sec x to evaluate tanx sec x dx 1 -sin 4x + C 32 -sin 2 x + + + C 1 sin 4x…

A:

Q: Suppose that a particluar funciton f satisfies f" (x) = - (4 sin(x) + cos(x)), f(0) = 3, f'(0) = 5.…

A: f"(x) = -(4sinx +cosx) ,  f(0) = 3 , f'(0) =5 now integrate the f"(x) f'(x) =4cosx -4sinx +c now…

Q: Prove that 2 Sin X dx 1 + cotx + cos x It tan X cos 2 x

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Q: Prove that _ d tanx = Sec'x.

A:

Q: Q4) Prove that dx 1+ 2 sinx || In √3 Χ tan tan x + 2 -√√3 +2 + √√3

A:

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.