Q1:- Prove that r(²-x) (² + x) - (1-x²) x. secxx 4 Hint Inf(1-n) = = sin (1/2 + x) ₁ TU sin næ π = COS TTX = 0

Q: 29. Show that sin x rif0<1 <2m.

A: Given a function sin x and 0&lt;x&lt;2π To show sin x&lt;x for all values of x such that…

Q: 13. To evaluate f 3cos*x-1 dx. the integrand can be transformed to 1-sin2x a. [(3cos x+ csc²x)dx b.…

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Q: -1 3. Show that sin-¹x = tan X √1-x² if |x| < 1.

A: Introduction: When there are trigonometric functions present in an expression or equation,…

Q: Prove that J5/2(x) = 2 TCX CScanned with CamScanner 3-x² 2 sin x - 3 COS X

A: Use the given information.

Q: prove that 2. = - Cotx + C 2 |- Cos?x + Sinx

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Q: Q96 h² sin² h o a) Show cos h - 1 = cosh + 1 h² o b) Use a standard trigonometric identity to prove…

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Q: 18 a Show that / (1 + sin 2zx)dx = n, for all positive integers n. b Sketch y = 1 + sin 27x, and…

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Q: (10,00 Puanlar) Let f(x) = sin 2x. Then find f (999) (x). a) 2099 cos 2x b) – 2099 sin 2x - c) –…

A: Given: f(x) = sin(2x) To find: f999(x)

Q: EVALUATE -dx + 144 ,2 O x – 12tan-1 12 none 1 -sin' 12 x – -1 +c 12 O x – tan-1 12

A: We have to evaluate  ∫x2x2 + 144 dx. We know,  ∫1x2+a2dx = 1atan-1xa + C      (where C is constant…

Q: 0 Prove for every x in the interval (0,1) the following inequality holds x² + sin² (ro) √T 1 + cos²…

A: We will use the basic knowledge of numerical analysis and applications of differential calculus to…

Q: 4. (a) Express 3cos x-4 sin x in the form R cos(x+ a) where R>0 and 0 <a < (b) Hence find the…

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Q: 1 1 Prove 2 csc? x 1- cosx 1+cos.x

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Q: . Let z = 1+ cos 0 + i sin 0, where - < 0 <0. (a) Show that |z| = 2 cos -1 and arg z = (b) Hence…

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Q: If x sinx < 1 2 - 2 cos x hold for all values of x close to zero. Find limx¬0 xsinx ? 2-2cosx

A: 1-x26&lt;xsinx2-2cosx&lt;1 holds for all values of x close to zero. Now, limx→01-x26=1-0=1 &amp;…

Q: Show that sin(x)  can be approximated by x-x3/6  within 0.01 on the interval [-1,1].

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Q: Find sin(8) O√3 -|~ 2 √2 2 이틀 2 TT 5T/6 7m/6 2/3 4/3 TT/2 3T/2 ○ TT/3 5/3 _TT/6 /11/6 0

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Q: 77. Find - Ans. (sin t – cos t + e-t) (8+ 1)(82 + 1) |

A: Topic:- inverse Laplace transform

Q: 2. Prove the following identities. = tan (x+2) 1tanr 1-tanx b) sin(π-x) - tan(-x) = sin2x c) secx =…

A: By the answering guidelines of Bartleby, We can answer only first three subparts, please post other…

Q: Q/ Evaluate the following functions 1.In(3-16) 3. cos ¹ (1+i 3) 2 (3|0.52) 2. e ‚4. tanh¯¹ (2-i5)

A: According to the given data, evaluate the functions:

Q: Madaurin f(x) = cos(7)

A: Find the Maclaurin expansion of  f(t)= cost

Q: -1 -1 18. Show that cos (-x) =T- cos x

A: We have to prove that cos-1(-x) = π - cos-1x

Q: Prove that: 3 (0) 2³ ( 1 - 4 ² ³ ; x ²) = + sin²¹ x (b) 2₁ (¹-x²) == tan²¹ x 1 H

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Q: sin 0-2 sin3 0 1. 2 cos30-cose = tan O 1 2. tan? x(1+ coť x) 1-sin2x 1 3. sec ( 2 cos'x) = 2x2-1

A: we have to prove

Q: Prove that there is a real number r so that sin(r) = x – 1.

A: We have, sinx=x-1 Let us consider a function fx such that, fx=x-1-sinx

Q: 71. Use Figure 4 to prove V1- 12 d /1 – x2 + sinx FIGURE 4

A: Let A be a point on a circle of unit radius(r=1) with origin as its center, such that: Calculate…

Q: -1 L-1 [wcose+ssine` s²+w² a. sin (wt + 0) b. sin (t + 0) c. cos (wt + 0) d. cos (t + 0) 2}, w & 0…

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Q: 9 Prove Sen 4t 4 cos3t sint-sin3t cos t.

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Q: 2- (a) Using [X, P] = ih, show that [X, PJ = 2ih& and [&, Þ³1= 2ihP. (b) Show that [, p2 = 2in(in +…

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Q: 3x-1 a) The function y=- has a horizontal asymptote at y = 3. x+2 b) cos x cos 4x-sin.xsin 4x=…

A: We have to decide whether the given  statements are true or false.