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

Q: Find all solutions to tan(x)=sec(x) that lie in the domain [0, 2)

A: tan(x)=sec(x) Given interval is [0, 2).

Q: f tan x = -5, and cos x > 0, find sec x and cos x 26 26 and cosx = 26 sec x = sec a = 26 and cos x =…

A: Solution-

Q: Verify the identity tanh2 x + sech2 x = 1

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Q: Verify the identity: sin(x - y)/(cos x cos y) + sin(y - z)/(cos y cos z) + sin(z - x)/ (cos z cos x…

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Q: Express tan a using x. 3

A: We have the right-angled triangle. Let us label the small triangle ABC, the big triangle ABD and the…

Q: Q2. Prove that sec2(tan-x) = 1+ x?

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Q: find maclurin formula in the fourth degree for f(x)=secx

A: To write the maclurin formula in the fourth degree

Q: In [tan (5 + )| +o sec x dx 4 2

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Q: 5. Evaluate tan (x)sec'(x)dx

A: Find the integral by using substitution

Q: Verify the identity: (sec t + 1)/tan t = tan t/(sec t - 1)

A: Multiply the left side of the equality by (sect-1) in the numerator and the denominator.

Q: . Evaluate sec z tan zdr

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Q: 4 tan(x) sec2 (x) tan(x) + 1

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

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Q: tan 2x sec 2x dx Evaluate cos 2x O 1 ,tan 2x e + C 2 2 e tan 2x + C O -2 e sec 2x + C 1 ,tan 2x + C…

A: ∫etan2x sec2xcos2x dx=∫etan2x sec2x sec2x dx     ∵secx=1cosx=∫etan2x sec22x dx Now put,…

Q: Find all 0 in the interval 0 <0 < 2T satisfying tan(0) = - 0. Give all answers as exact values…

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Q: Find f tan 0 de. ] a. C. - In sin 0+ C - In cos 0+ C sec² 0 + C - In sec 0 + C

A: Here we have to solve the integral.

Q: Evaluate / 5 sec2 *dx tan(x) 05 In(|tan(x)|) + C Oln(tanx) + C 05 In(x) + C 05 tan(x) + C

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Q: State the Mean Value Theorem. Use it to show that for all x ≥ 0, 0 ≤ tan^−1 x ≤ x. [Hint: Use Dx…

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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: Let S(x) 9 sin x + 9 cos x "(x) 3= r(-)-

A: A function is given as fx=9sinx+9cosx. The objective is to find the first derivative f'x of the…

Q: If 1, = | x" sin x dx, prove that 1, = nx"-! evaluate -1,. sin x- x" cosx– n(n-1)I, 2. Hence, = NX…

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

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Q: Show that the two formulas are equivalent                                                      ∫tan…

A: To show that ∫tanx dx=-lncosx+C and ∫tanx dx=lnsecx+C both formula are equivalent. We know that…

Q: Evaluate sec z tan a da- 0. 114

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Q: If f(x) = 2 tan '(5 sin(3r)), f'(x)-

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

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Q: 1 If f(x) = 8 tan¯¹(8 sin(2x)), f'(x) =

A: Differentiate

Q: The derivative of In (cos x) is A -tan x B None of the given choices tan x D sec x -sec x

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Q: Verify the identity: sec x - 1 = sec x 1- cos x

A: Now , we will verify the identity.  We know,  1/cosx = secx .

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: In(|tan(x) sin(x)|) = 2 In(|sin(x)]) + In(|sec(x)])

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

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Q: x=cos¬! 1 prove that sec" X= cos

A: Given sec-1x=cos-11x

Q: If A = [0, 2π] and A is measurable, prove that lim cos nx dx = lim [₁ sin nx dx = 0. n-∞ JA

A: Given that if A⊂0,2π and A is measurable, the objective is to prove that limn→∞ ∫A cos nx dx =…

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

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Q: 1 .Prove that : sec q + tan q = 2x or, 4x If sec q = x+ 2x

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Q: Factor.

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Q: (1+ tan(z)) sec² (x) dx

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Q: 3) Prove that b) tan- (*)} = sechx

A: Evaluate the derivative of the given function as follows. ddxtan-1ex=11+ex2ddxex…

Q: 4. Prove that tan x – cos x = sec x – cosʻ x - x- cos cos x – 1. :

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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…

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Q: How many periods of the function y = sec x are there between = and 3T -

A: Given: So, from the figure, it can be observed that only one period of y=sec x is there between -π2…

Q: Q4: Prove that: secx * cscx = tan x + cot x %3D

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

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Q: a. Show that y = tan u increases on every open interval in its domain. b. If the conclusion in part…

A: (a)  Given,

Q: Show that:- tan-1 x + tan-1 y = tan-1 x+y 1-ху

A: We need to show the following identity tan-1x + tan-1y = tan-1x+y1-xy

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

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Q: (a) Show that lim | x| cos = 0.

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: