EXAMPLE 6 (a) Show that sin-1 (sin (4)) = - (b) Show that sin-" (sin ())+ + *. (b) Show that sin¬l (sin 5л 5л

Q: 1 -sin(2x)% = (D²-1 -1 sin(2x) 125 O ibs

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Q: O yotan' (x'+3x-s)+ sin (x²s 2x -1)

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 1 cos(5x) +... 25 cos(x) + cos(3x) + Ans. + 2 sin(x)+ sin(3x) +sin(5x) +...

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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: 4. cos*x Evaluate: sin' x( sin' 3/5 x+ cos³ x 3.

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Q: If e/2i -/2i = sin2 then z = - 2i In(sin2) – 4kn 2i In(sin2)+ 4kT - 2i In(sin2) + 4kTt

A: Given: e-z2i=sin2

Q: gral. cos 7x cos 4x dx ㅇ응 cos 3x + 숲 cos 11x + C ㅇ sin 3x + sin 11x+C 1 sin 3x - sin 11x +C

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Q: 2. 1.5 sin(3t-

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Q: cos 2x–1 lim COS х— 1 cos x-1

A: limx→0cos 2x-1cosx-1

Q: 2 2 In sin 2x - 2 In (1 + cos 2x) = In ( )- %3D

A: Given that: The identity is 2 ln sin 2x - 2 ln ( 1 + cos 2x) = 2 ln tan x .

Q: cos(4x) – cos(8x) tan(2x) tan(6x) cos(4x)+ cos(8x)

A: We have to proof

Q: Find * sin (In æ) cos²(ln x) dx. cos (In x) , cos³ (In x) 3 cos (In x), cos³ (In x) 5 3 5 Option 3…

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Q: 5) 3tan-1x + sin-x = 4

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Q: 15. 2sin3x + sin²x - 2sinx -1 = 0

A: Given equation, 2sin3x+sin2x-2sinx-1=0

Q: Chapter 6, Section 6.3, Question 012 Use the Fundamental Theorem to evaluate the definite integral…

A: Given,

Q: 7. cos 2x- cos x -2 = 0

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Q: limx→0 (1−cos(5x))/(1−cos(9x))

A: Used L'Hospital rule

Q: sin(4x) cos(2x) dx = cos (2x) cos (6x)' sin (2x) cos (2x) сов (10х) 4. (2x) sin (10x)+ c sin +c 10…

A: Use formula 2sinAcosB=sin(A+B)+sin(A-B)

Q: Evaluate sin 2x sin 4.xdx 2 b. sin 3 2x + C 3 1 a. sin ' 2x+C 3 c. cos' 2x+C 1 с. 3 d. -cos 2x +С 2

A: To evaluate the given integral: ∫sin 2x sin 4x dx

Q: 1 1 Express in terms of csc(x) 1+ cos x 1- cos x

A: Given:     To determine: The given expression in terms of cscx

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 0 and cos 0 if tan 0 sin = 3/5 sin = -3/5 sin = 4/5 sin = -4/5 cos = 3/5 cos = -3/5 cos =…

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Q: 11) cos x csc X tan x - 1 11) 12) cos2x - sin2x = 1 - 2 sin²x 12)

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Q: Example 2: find ỹ,y=sin-1 Vx.sec-1 (sin x) Example 1: find ỹ,y=tan-1(x². sin x) Example 3: prove…

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Q: 1 sin(2.x): sin(2x) -125 %3D (D²-1)' true false

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Q: 4. 1-3 cos x-4 cos² x 2 sin² x 1-4 cos x 1- cos x

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Q: EXAMPLE 2 Differentiate (a) y = sin(x³) and (b) sin3(x). SOLUTION (a) If y = sin(x³), then the outer…

A: Given:-(a) y=sin(x3)(b)y=sin3xwe have to differentiate(a) y=sin(x3)differentiate with respect to…

Q: 51 |x* sin 3xdx 2 53 [x' sin 3xdx 55 sin 3xsin 2.xdx

A: As per the guidelines I am supposed to do the first question among multiple questions. So I am doing…

Q: (sin 31)8(1-a/2)dt

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Q: verify sin2(x)+cos2(x)=1

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Q: Establish the identity.

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Q: 1 3n sin 3x + 3. |-23 8.

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Q: 1) f(x) = x5-x¹ + x² - x +² 2) f(x) = sin³x - e³x² + ln(1 + 5x²) 3) f(x)=√1-x² sin-¹ x 4) f(x)=√√x +…

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Q: 1 sin(2.x) = -sin(2x) -125 %3D (D²-1)' true false

A: Solution

Q: Q1-6 * 2 points 1 -sin(2x): - sin(2x) -125 (D²-1)'

A: Given, 1D2-13sin2x=x-125sin2x To find:  To check whether L.H.S = R.H.S. or not

Q: cos4x - sin4x = cos 2 x 2 cos 2 x -cos 2 x

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Q: sinh- x = In 2.

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Q: sin 0 13. Prove that 1 - = Csc 0(1 + cos 0). Cos 0

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Q: sin 4.4- sin 2A (a) Verify that = tan A cos 4.4 + cos 2.4 (b) Express the following as a product of…

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Q: Prove: sin² x + 2 cos²x − 1 = cos²x -

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Q: sin 2x sin x Cos 2x %3D Prove that 4 cos x - sec x Cos a

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Q: Verify the identity. 9 cos(sin ¹ x) = √81 - 81x² = 8 = x = . Thus, Let 8 = sin-¹ x = sin 8 = x 9…

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Q: Scos“ x- sin' xdx x•sin³ xdx 3

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Q: Verify the identity. sin 5x + sin 3x 2 cos x 4 sin x cos3 x - X – 4 sin x cos x 3.

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Q: sin(4 + 5x) cos (5x – 4)dx

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Q: 15. f(x)= sin 3x 17. f(x)= tan 2.x 19. f(x)= 3 cos (x – 7/2) -

A: 15) For sin(3x) the range of the function will  be the same as sin(x) just the period, in this case,…

Q: 5) 3tan-1x + sin-1x = 4

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Q: sin- In2| 4+ tan¬'cos- dx 2 2 1+ cos- |4+ tan-'cos= 2 2sin- In2| 4+ tan-'cos- |dx 2 2 A 1+ cos2…

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Q: Prove that X -sin 8 2 X sin sin x 8 2 2. 2.

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