Chapter 5 True Or False and Multiple Choice Problems 1 For each of the following ten statements answer TRUE or FALSE as appropriate (a) If f is di↵erentiable on 1,1 then fSin2(x) cos2(x) = 1 tan 2(x) 1 = sec (x) DoubleAngle Formulas sin(2x) = 2sin(x)cos(x) cos(2x) = cos2(x) sin2(x) cos(2x) = 1 2sin2(x) cos(2x) = 2cos2(x) 1 1 1(12 points) Determine whether each of the following statements is True or False True False Solution False If f(x) = 1 2x, then fsatis es that 0 f(x) < 1 x for all x 1, but Z 1Question The trigonometric function tan 8 In terms of sec @ In the ill quadrant is vi100 False Determine whether the statement is True or False 5 poin 2x' 5x2, 2x* x =1 Consider x>1 3x2 7x2 3x² x True False Determine whether the statement is True or False 5 points An equation of the line passing through the point (1,1) and
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Tan 1 p tan 2 1 sec2 d = Z tan 1 p sec sec2 d Remember to think carefully about the p sec2 part From here we can proceed as normal (assuming sec is positive, just for simplicity) = Z tan 1 sec sec2 d = Z tan sec sec d And we've successfully reduced the problem to an integral we can do Ivan Khatchatourian MAT137 1 February, 18 7 / 31The Pythagorean identity sin^2(x)cos^2(x)= 1 is useful in proving the identity tan(x)sec(x)= (cos(x)/(1sin(x))) true or false Answer by stanbon(757) ( Show Source ) sin^2 (x) cos^2 (x) = 1 everywhere An alternate approach to proving this identity involves using the "unit circle" (radius = 1) Since the radius is
It is a trignometrical identity, there is nothing there to solve The identity is arrived at by simplifying the identities in sin(x y) cos(x y) = sinxcosy cosxsiny cosxcosy − sinxsiny Divide the numerator as well as the denominator by cos x cosy to get tanx tany 1 − tanxtany Answer link 1 = (sec(x)) 2 (tan(x)) 2 Now, we will see if 1 = (sec(x)) 2 (tan(x)) 2 and 1 = (sec(x)) 2 (tan(x)) 2 can both be true We can do this by assuming that they are both true, and then add the equations to get Tan^2 x1=sec^2x So to get 1 on the other side of the equal sign wouldn't it be sec^2xtan^2x=1?Get stepbystep solutions from expert tutors as fast as 1530 minutes Your first 5 questions are on us!1 A water molecule is held together by two single polar covalent bonds False 2 Because oxygen has a greater electronegativity than hydrogen, water molecules are polar with Biology These are true and false questions and I want to make sure that I got them right 1
tan^2x sin^2x (sec^2x 1)(1cos^2x) sec^2x 1 1 cos^2x 1/cos^2x 2 cos^2x (1/cosx cosx)^2 God luck with that Or use your doubleangle formula a couple of times tan^2x sin^2x cos^2x = (1 cos2x)/2 sin^2x = (1 cos2x)/2 You wind up with (cos4x 4cos2x 3) / 4(cos2x 1) Use your halfangle formulas for the other oneFind the second order derivatives of the following e2x tan x Mathematics and StatisticsHere f = cos 2 x and g = tan x To differentiate f, we need to use chain rule \(\frac{d}{dx}\) (cos 2 x tan x) = tan x\(\frac{d}{dx}\) (cos 2 x) cos 2 x\(\frac{d}{dx}\) (tan x) \(\frac{d}{dx}\) (e x tanx) = tan x(2 cos x sin x) cos 2 xsec 2 x At x = 1 we get, = tan0(2 cos 0 sin 0) cos 2
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= sin x cos x sin 2 x cos 2 x We know that sin 2 x cos 2 x = 1 Therefore, = sin x c o s x 1 = sec x cosec x Hence, proved We have, = sec 2 x c o s e c 2 x = cos 2 x 1 sin 2 x 1 = sin 2 x cos 2 x sin 2 x cos 2 x = sin 2 x cos 2 x 1 = sec 2 x c o s e c 2 x Hence, proved Since ≠ for all values of the equation is not an identity x − 2 x 1 sec 4 sec 2 x tan 2 x cot 2 x − 2 x 1 sec 4 sec 2 x tan 2 = (x −1)(x −1) sec 2 sec 2 x tan 2 = x ⋅ x tan 2 tan 2 x tan 2 x tan 2 x − 1 sec 2 = x tan 2 x tan 2 x cot 2 x, Page 1 of 12 PRACTICE TEST 61 tan^2xsec^2x=1 true or false?
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Thus, the required derivative is {eq}\bf{\dfrac{2\tan(x)\arctan(2x) \sec^2(x)(14x^2)}{\tan^2(x)(14x^2)}} {/eq} Become a member and unlock all Study Answers Try it riskfree for 30 days Free PDF Download of CBSE Maths Multiple Choice Questions for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions Maths MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern Students can solve NCERT Class 12 Maths Inverse Trigonometric Functions MCQs Pdf with Answers to know theirAnswer the following questions TRUE or False If f has a vertical asymptote at x = 1 then lim x → 1f(x) = L, where L is a finite value If has domain 0, ∞) and has no horizontal asymptotes, then limx → ∞f(x) = ± ∞ If g(x) = x2 then lim x → 2 g(x) − g(2) x − 2 = 0
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Determine if the following equation is true or false {eq}tan^2(x) 1=sec^2(x) {/eq} Trigonometric Identities The trigonometric identities are tools that we can use not just to simplify anIf x sin 3 θ y cos 3 θ = sin θ cos θ and x sin θ = y cos θ, prove that x 2 y 2 = 1 View Answer If tan θ = 3 − 2 , find sin 2 θ sec 2 θ − c o s 2 θ(tan x csc 2 x tan x sec 2 x) (1 tan x 1 cot x) For the following exercises, determine whether the identity is true or false If false, find an appropriate equivalent expression 40
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1/(x y) = 1/x 1/y answer choices True False s Question 10 sec x tan x sec 2 x sin x arctan x s Question 27 SURVEY 30 seconds Report an issue Q Differentiate y = (x 3 1) 100 answer choices 300x 2 (x 3 1) 99 99(x 3 1) 98 100(x 3 1) 99 100(3x 2) 99 s Question 28 SURVEY 30The functions sine, cosine and tangent of an angle are sometimes referred to as the primary or basic trigonometric functions The remaining trigonometric functions secant (sec), cosecant (csc), and cotangent (cot) are defined as the reciprocal functions ofTrue or false 4)Graph of f(x) = cosec(x) has 2 vertical asymptotes in one period true or false 5)The amplitude for f(x) = 3sec(4x) is 3 true or false 6)f(x) = 2 sec(2xπ) has A Period =
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Tan^2 (2x) 1cos (6x)= 2sin^2 (3x) (true or false) sin (75 degrees)=sqrt (1cos (150 degrees)/2) true (TRUE or FALSE) The horizontal distance, in feet, traveled by a projectile can be modeled by the equation h = ( (v0^2)/16) sinθcosθ where θ is the initial angle and v0 is the initial velocityExtensions For the exercises 3439, prove or disprove the identity 34) \(\dfrac{1}{1\cos x}\dfrac{1}{1\cos (x)}=2\cot x\csc x\) 35) \(\csc^2x(1\sin^2x)=\cot^2x\) True or false The equation csc^2x1=cot^2x is an identity
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Tan 1(2x) dx= xtan 1(2x) 1 4 lnj1 4x2j Cusing IBP R e 1 x3x1 x dx= (e3 1)=3 eby dividing rst and ln(e) = 1, etc lim n!1cos(2ˇn) = 1 because cos(2ˇn) = cos(0) = 1 P 1 k=1 (1 2 1 3) = 1 3, telescoping (write out a few terms) R tan3(2x)sec(2x) dx= sec 3(2x) 6 sec(2x) 2 Cusing u= sec(2xMathematics Multiple Choice Questions on "Derivatives" 1 Find the derivative of e x 2 a) e x 2 b) 2x c) 2e x 2 d) 2xe x 2 Answer d Clarification We apply chain ruleTrigonometric Identities Solver \square!
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Find an expression equivalent to cos theta/sin theta tan theta cot theta ~ sec theta csc theta 3) cos 3x / cos x = 2 3 1 cos x/ sin x= sin x/ 1 cos x 4 2 sin x cos ^2 (x/2) 1/x sin (2x) = sinx 5 cos 2 x sin x/ 1 sin x= 1 2 Math sin x multiply by csc x= 1 true or false?Csc 2 x sec 2 x sin 2 x 1 sin 2 x s Report QuizMath Cheat Sheet for Integrals \mathrm{If\exist\b,\a\lt\b\lt\c,\and}\f\left(b\right)=\mathrm{undefined},
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