Q1/ Answer the following: (a) Show that sin-x + cos-1x = " 2 x(x-y) (b) Find the value of tan-1 tan-1 2, where >-1 y(x+y)

Q: for the equation 8x(x−1) +cos(x) =0 does the intermediate value theorem show at least one solution…

A: Let, f(x)=8x(x−1) +cos(x) 8x(x−1) and cos(x) both are continuous for all real values of x. So, f(x)…

Q: Use the False Rule method to find a solution for the function sin (r) = x ^2 - 1. With an accuracy…

A: Given,          sin(x)=x2-1

Q: S./2(sec²x – cos²?x – tan²x)sin5xcosxdx -

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Q: Q4// Find the value of csc(sec-1 2) + cos(tan=²(-V3)).

A: Here  given as Use some trigonometric formula as

Q: Solve sin(x) +7 sin(x) cos(2x) = 0 for x E (0, 5). Give your answer in radians correct to 3 decimal…

A: The given equation is sin(x)+7sin(x) cos(2x)=0 and the range for x is (0, π/2).

Q: 3. Express 1+cos2x in terms of cos x. hence a. Evaluate (1 + cosx)dx b. Express 1- cos2x in terms of…

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Q: Estimate the error if P 3(x) = x - (x^3/6) is used to estimate the value of sin x at x = 0.1.

A: Given:

Q: |6. Determine two values of x between 0° and 360° that have sin x 2

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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 sin2x and cos2x, given that tanx=-4/3, and pi/2 less than or equal to x less than or equal to…

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

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Q: Q5/ If tan 0 :- find without using table values of: sin 0, cos 0.

A: The given question is taken from trigonometry and calculus so we have to deal with both of the given…

Q: find the approximate values for all solutions to tan^2t -tan t -6 =0

A: Obtain the approximate values as follows.

Q: 2x, given tan x= 2 and cos x is less than 0

A: Given tan x = 2 and cos x < 0.

Q: 3. Express 1++cos2x in terms of cos x. hence a. Evaluate (1+ cosx)dx b. Express 1- cos2x in terms of…

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Q: Find ∫sin3 x cos4 x dx.

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Q: 2. Find the exact value a. sin'' -1/2 b. arccos - с. tan-1(tan - )

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Q: dr de sin - r- cos + eª cos = 0

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

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Q: Find cos(4x) sin(4x) da.. To cos(4x) sin(4x) dx : =

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

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Q: Solve the equation on the interval [0,2x). cot x(tan x+ 1) = 0

A: Equations involving trigonometric functions can be solved by simplifying the equation first and then…

Q: Evaluate 2 sin² x cos³ x dx 0,

A: Given that: ∫0π2sin2x.cos3xdx

Q: Complete the statements.

A: Given Our aim is to complete the sentence

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: Find sin(2x), cos(2x), and tan(2x) from the given information. 3T 2 sin(2x) sin(x) = = cos(2x) =…

A: We have to solve above question and find sin cos and tan value

Q: Find sin 2x, cos 2x, and tan2.x if sinx= -- 3 and x terminates in quadrant IV. V13 sin 2x cos 2x tan…

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Q: Solve the equation on the interval 0s0<2n. 3 tan 0+ 1 = 0 What are the solutions to 3 tan 0+ 1 = 0…

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Q: .2 Determine the value of sin x + cos x for x = 30 degrees.

A: The given expression sin2x+cos2x for x=30 degrees.

Q: 5. Solve for the values of sin2x, cos2x and tan2x when tanx = 1, on 0 ≤ x ≤

A: Given that,    tanx=12, on 0≤x≤π2

Q: Find a value of x that satisfies the equation sin 20o cos (x).

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Q: tan-+ 4 +V3 = 0

A: Given  [ 0

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

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

Q: Find all values of x in the interval [0, 2π] that satisfy the equation.  sin x = tan x

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Q: Solve the equation on the interval 0s0<2n. tan (20) +2 sin 0 = 0

A: Consider the equation tan(2θ) + 2sinθ = 0 on the interval 0 ≤ θ ≤ 2π.

Q: Refer to the graph of y = sin x or y = cos x to find the exact values of x in the interval [0, 4p]…

A: Sketch the graph of function y=sinx as shown below.

Q: Suppose y=sin x, what is x-value between 2pi and 4 pi corresponding to y-value of -1

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Q: determine the value of sin^2 x + cos^2 x for x =10 degrees

A: Given x= 10 degrees By trigonometric formula we know that , sin2(x)+cos2(x)=1 where x∈-∞,∞

Q: Find the linear approximation of f(x)=sin(x) at x=3π4 and use it to approximate sin(134∘). Give…

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Q: Why is I cos 0 |never greater than 1 in the first place?

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Q: 10. Evaluate cos x sin² x dx

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Q: 5. If x = 3tan 0, find sin e in terms of x.

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Q: y = cos (tan (3x)) A. -9cos? (tan (3x))sin (tan (3x)) sec (x) B. -9cos? (tan (3x))sin (tan (x))…

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Q: Where does the periodic function ƒ(x) = 2e^(sin (x/2)) take on its extreme values and what are these…

A: Given,

Q: Find a root of  x- sin(x) - (1/2)= 0 correct to four decimal places by Secant Method

A: The given function is: x-sinx-12=0 Let, fx=x-sinx-12 Here, f0=-0.5f1=-0.3415f2=0.5907

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

A:

Q: In sine sin -1x os (sin-!x) + C cos V1-x? 1-x² A) True В False

A: To check:  ∫sin(elnsin-1x)dx1-x2=-cos(sin-1x)+C is true or false.