Q1/ Answer the following: (a) Show that sin¬'x + cos-1x x(x-y) ), where- -> -1 y(x+y) (b) Find the value of tan¯ tan

Q: The derivative of any constant is 0. The well-remembered triq identity tells us that sin2(x) +…

A: To verify that sin2(x) + cos2(x) is a constant, we need to show that the derivative of sin2(x) +…

Q: The value of 1 cos (tan ¹y) + y sin (tan¯¹y) cot (sin¯¹y) + tan (sin¯¹y) is......... +y¹

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Q: 7. Show that sin E + x) = G+x): = -cosx.

A: Introduction :

Q: -1 We can conclude from the derivative of sin-1(x)and cos-1(x) that sin-(x) + cos¯(x) is constant.…

A: Explanation: find the derivative of sin-1x & cos-1x

Q: 1. Differentiate the following with respect to the variable given. 1 cosx 2 sin' x tan

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Q: If sin x - cos x = 1/5, what is (sin x) (cos x) equivalent to?

A: Given sinx-cosx=15Squaring the equationsin2x+cos2x-2sinxcosx=125

Q: The suitable substitution to evaluate / sin²4(x +2) dx is (1- cos8(r + 2)] [1+cos8(x+2)] None 1 [1-…

A: We have to find the suitable substitution to evaluate the following integral -  ∫sin24(x+2) dx

Q: 1 Differentiate y = tan 8x + cos ,x

A: Using differentiation rule,

Q: Show that L-1{ = (sin hat sin at) s4+4a4, 2а2

A: To find Inverse Laplace transform of ss4+4a4: write ss4+4a4 as  ss2+2a22-2as2 Then the denominator…

Q: Find the coordinates of the point on the graph of y = 8 sin x+4 cos (2x) + 14, 0 <x<5, where the…

A: Consider the given function, y=8sinx+4cos2x+14 The slope of the tangent line on the given curve will…

Q: Q#2 (a): Find root of the equation 3x + sinx – e* = 0 by secant method correct to six decimal Places…

A: # we are entitled to solve 1 question at a time ,please resubmit the other question if you wish to…

Q: EX-15- Prove that : a) Sec-'x= Cos- ! b) Sin-' (-x)=-Sin-'x

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Q: Find the slope of the tangent line to the sine function at the origin, (a) y = sin(4x) 15 y'(0) = 4…

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Q: Differentiate a $sin "(z) with respect to sin x.

A: We will find out the required value.

Q: Obtain graphically an approximate value of the lowest root of cos x cosh x =- 1.

A: The equation cosxcoshx=-1 regulates the frequency of vibration of a cantilever. We must first…

Q: 3. Find S sin5 x cos* x dx.

A: Use substitution method

Q: The derivative of y = 3 cos (V1-x²) + (1-x²), can be written as sin ( V1-x² ) – ( 1–x²) }) 3x…

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Q: f'(t) = sin 8t - cos -/-

A: You are correct

Q: /2 Evaluate sin 20 de sin20 x+ cos x 20

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Q: 1 Differentiate f(æ) = sin-(4x). Use exact values. = (x),f

A: We use the chain rule for differentiation

Q: Evaluate cos x -2 sinx sin 2x dx Round to 4 decimal places.

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Q: If z =7 tan 0, express sin (20) as a function of z. sin (20) =

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Q: 1. Differentiate the following with respect to the variable given. 1 cosx 2 sin x tan 2. Given the…

A: We can solve the given problem as follows:

Q: Suppose: sin(x) = -0.1 cos(y) = 0.5 tan(z) = -4.3 Then, sin(-r) =| 0.1 cos(-y) = 0.5 tan(-2) = 4.3…

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Q: Find the equation of the line tangent to the graph of f(x) = -2 sin (x) – 1 at'x = =. (Enter an…

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

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Q: verify that (sin(x)-cos(x))^2=1-sin(2x)

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Q: Use a calculator to compute sinh x and cosh x for x = −3, 0, 5.

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Q: (i) Prove that sec 3x(sin 3x-2sin' 3x)= tan 3xcos 6x. (ii) Hence find, for 0s.xs, the values of x in…

A: Trigonometric equation

Q: 12 tan (4.x) sec (4x) dx S cos(11x) sin(2r) dx COS

A: Given that integration and we solve this integration by using general formulas of integration. Here…

Q: Use sin 0 = 0, sin = 1, and sin t = 0 to estimate sinl E) (Round your answer to three decimal…

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Q: Differentiate f(x) = sin-(2x). Use exact values. f'(x) =

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Q: Differentiate  x sin−1(x)  with respect to sin−1x.

A: Using derivative of one function w r to another function.

Q: Find sine half range for f(x) = \cos xl for -1<x<1 COSX for 7 < x < 0. f(x) for 0<x< 7. COSX

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Q: Choose the correct answer If f(x)=ln⁡(cos⁡(3x)) , then f"(x) =…  -9 sec2 (3x)  9 cos2 (3x)  9 tan2…

A: Derivative problem....

Q: Find the second derivative of f (z) = 6 sin (4z). %3D Enclose arguments of functions in parentheses.…

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Q: The derivative of sec² 2x (cos² r - sin² x) with respect to a is O2 sec 2x tan 2x O4 sec² 2x cot 2x…

A: Find the derivative

Q: sinx f(x) = on [0, 2n] cos x-V2

A: Given :         f(x) = sin xcos x - 2 on 0, 2π   To determine the extrema of the above function…

Q: 4 dx 1– cos(4x)

A: We to evaluate the integral ∫4 dx1 - cos 4x

Q: Find sine half range for f(x) = \cos x for -t< a <n %3D cosx for f(x) for 0<x <n. cosx

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Q: Differentiate f(x) = sin'(7x). Use exact values. f'(x) =

A: Explanation of the solution is given below...

Q: Differentiate x sin-1 (x) with respect to sin¯'x. х.

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Q: Show that, for real values of x, 3 sin x f(x) 2 + cos x cannot have a value greater than 3 or a…

A: To show that the minimum and maximum value of the function is -√3 and √3

Q: Evaluate: cos x-sin(sin x)dx and explain your answer in terms of odd/even functions.

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Q: Find sin (x/2) cos(x/2) tan(x/2)

A: Given information is :

Q: Evaluate the indefinite intergral ∫sin(-10x) dx =

A: This question can be solved using integration by substitution.

Q: Find x cos(x)-sin(x) = 0

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Q: a(cos2x) sin(x-) TC 1. f(x) = tanx 4. What values should a and b take for the function fx) to be…

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