A tangent reduction formula Prove that for positive integers n + 1, tan"-x п — 1 tan" x dx tan" -2x dx. Use the formula to evaluate 4 tan x dx.

Q: Prove that the inequality sinx+tanx>2x holds in the interval (0,π/2).

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Q: Let f (x) = 6 sinh 1(tan(x) , O < x < 5. Find the slope of the line tangent to the graph of f at the…

A: Given: Here, we need to find the tangent line to the graph of f at the point on its graph where…

Q: If f(x) = cos x – 7 tan æ, then f'(z) -sin( x ) – 7 sec²(x) = f'(2) =

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Q: Find the indefinite integral.

A: We have to solve the indefinite integral: ∫tan x3 sec2 x dx Solving the integral by substitution…

Q: Evaluate the integral. ∫0 π/3 tan5 x Sec4 x dx

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Q: 2. True or False. The dx [Arctan(tan x)] = 1 for all x in the domain. ans. True

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

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Q: The trigonometric integral fs sec² x (tan³ x - 2 tan7 x) dx is equal to

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Q: Estimate the values of limit (tan 2x)/(sin x) as x approaches 0; Estimate the values of limit (tan…

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Q: Evaluate the indefinite integral. 4 tan°(x) sec*(x) dx

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Q: A tangent reduction formula Prove that for positive integers n + 1, tan"-lx - Jun-sdt. tan“ x dx n -…

A: Given tangent reduction formula is: ∫tann x dx=tann-1 xn-1-∫tann-2 x dx We have to find the integral…

Q: Find the indefinite integral ∫ 3√(tan x) sec2 x dx

A: ∫tanx3sec2x dx Now put tanx=t⇒sec2x=dtdx⇒sec2x  dx=dt

Q: find integral tan 3 x dx

A: To find the integral of tan2x first split tan into two part and the using property of sec and tan…

Q: If y = f (x) = In (cosx), then, f' (x) =? O tan (x) O-sinx (x) -tan (x) O-cot (x)

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Q: DO NOT include spaces in between characters. * = <x<0. Given that tan 2r =-2, solve for tan x. 4 Let…

A: The given data is: tan2x=-2, -π4&lt;x&lt;0 Solve for tanx.

Q: d -(tan²(x) - dx 1 Prove that : 1+x*

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Q: Find the indefinite integral ∫tan3 x/2 sec2 x/2 dx

A: we have to find the value of indefinite integral  ∫tan3x2sec2x2dx let the given indefinite integral…

Q: E prove that = - Cotx + C %3D 1- Cosx +Sin'x

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Q: Let f(x)= ln(e^x +2x) -2 Find equation for tan line at x=0

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Q: Evaluate the indefinite integral.

A: Consider the given integral I=∫sec3x·tanx dx

Q: Which equation represents a tangent function with a domain of all Real numbers such that x 2…

A: We know that the domain of the tangent function tan x is: all real number x except x≠π2+nπ , n∈ℤ

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: 3. Prove the identity : sin(x- y) tanx - tany cosxcosy

A: The given identity is, tanx-tany=sinx-ycosxcosy The identity will be true if the left-hand term will…

Q: Using suitable method, show that 2 tan" (x+2) dx =- – In 2 .

A: We use integration by parts to find integral tan inverse x.

Q: Find the indefinite integral ∫tan5 x sec4 x dx

A: Given:∫tan5(x) sec4(x)dx

Q: Evaluate the integral. 2 tan (x) sec(x) dx (Use symbolic notation and fractions where needed. Use C…

A: Consider the integral

Q: 91. Prove the integration formula tanx dx = In | secx| + C (a) by using algebra and integration by…

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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: y=tanu Differentiating with respect to u, we get dydu=sec2u Now clearly, sec2u≥0 for every value of…

Q: If f(x)=tan x, then show that f(x+y)-f(x) = sec^2x tany/ 1-tanxtany

A: The detailed solution is given below Thank you

Q: An appropriate trigonometric substitution 1 -dx is V4 – x² for x = 2 tan(8) for 0 E (-5,5) а. b. x =…

A: The given integral is: ∫14-x2dx

Q: Evaluate | tan (3x) sec*(3x) dx. EXAMPLE 5 If we separate one sec2(3x) factor, we can express the…

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Q: tan' (x) sec (x) dæ

A: We have to evaluate the indefinite integral.

Q: Use u-substitution to evaluate the integral: (cos(x)/ sin(x)+1) dx

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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: Prove that the inequality sinx+tanx&gt;2x holds in the interval (0,π2).

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

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Q: Find the indefinite integral (2 sec x tan x +9 sec? x) dx. |(2 sec x tan x +9 sec? x) dx =

A: Integration appling rule constent cofficenat.

Q: Prove that? 2tanX tan 2X %3D 2 1- tan x

A: Given : 2tanx1-tan2x = tan2x

Q: Example : Find an approximation to zero of tan(nx) – 6 = 0, in [0, 0.48]by Secant Method.

A: To approximate the zero of f(x) using secant method.

Q: estion 46 of 60 What are all values of x in the interval 0, for hich (tan x)(2 sin x 1) = 0 ? - Pre…

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Q: Evaluate the definite integral. Use a graphing utility to verify your result.

A: Given:                   ∫0π4sec2θtan2θ+1 dθ   Solution:               We can find out the solution…

Q: The trigonometric integral [sec² x (tan³x - 2 tan² x) dx is equal to

A: SOLUTION-

Q: Evaluate the integral. "1/3 tan (x) sec*(x) dx

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Q: What is special about the functions ƒ(x) = sin-1 (1/ sqrt(x2 + 1))  and g(x) = tan-1 (1/x)?…

A: Given functions are

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

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Q: Prove the identity : sin(x-y) tanx- tany Cosxcosy

A: Consider, tanx-tany=sinxcosx-sinycosy=sinx cosy-cosx sinycosx cosy=sinx-ycosx cosy…

Q: Find 2 sin(x + sin(x + sin a)) – 2 cos(cos 1) lim 2x – T ithout using L'Hôpital's Rule.

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