Write the expression as an algebraic expression in x for x > 0: sin(2sin' x)

Q: Use the addition formulas to derive the identities

A: We will use cos(A-B)=cosAcosB+sinAsinB formula with A=x and B=π/2

Q: Write the expression as an algebraic expression in x for x > 0.

A: Since, we know that cos2 (x)=cos (2x)+12⇒2 cos2 (α)=cos (2α)+1By assuming α=12(cos-1x)⇒cos 12cos-1…

Q: if x+1/x=2,find sin-1x

A: Given,

Q: Evaluate the integral ∫sin5 x/3 cos x/3 dx

A:

Q: L[sin bd]- show that

A:

Q: Give an example of a value of z such that the equation sin(x ) = z is unsolvable.

A: We have to give an example of a value of z such that the equation sinx=z is unsolvable.

Q: Write an algebraic formula for sin[(sin^-1(u)-cos^-1 (v)]

A:

Q: Evaluate the integral ∫sin x/4 cosx/3dx.

A:

Q: In each part, rewrite the expression as a ratio of polynomials. (a) cosh (ln x) (b) sinh (ln x) (c)…

A: a)  Given expression is cosh ln x. As cosh x=ex+e-x2 So, cosh ln x=elnx+e-lnx2=elnx+elnx-12=x+1x2…

Q: Prove the identity (sin x - cos x)2 = 1 - sin 2x

A:

Q: Sin-l e

A:

Q: Prove the identity.   (cosh x + sinh x)n = cosh nx + sinh nx  (n is any real number)

A: The cosh x and sinh x are given by, LHS =

Q: evaluate the definite integral of " sin^2{x} " from [-pi, pi]

A: We will use the reduction formula to solve given definite integral

Q: Prove the identity. sin(x+y) sinx + cos(x+y) cosx = cosy

A:

Q: Verify the identity sinh x + cosh x = ex

A: To prove the identity

Q: Write ∫ tan2k+1 x dx, where k is a positive integer, in terms of ∫ tan2k−1 x dx.

A: Given integral is ∫tan2k+1dx. Rewrite the above integral as follow.…

Q: Evaluate the indefinite integral. ∫sin5(x)cos4(x)dx

A: Integrate the given indefinite integral as follows.Consider the expression sin5(x)cos4(x).The above…

Q: Prove the identity sinh 2x = 2 sinh x cosh x

A: Prove that: sinh 2x = 2 sinh x cosh x

Q: Estimate the error if P3(x) = x - (x3>6) is used to estimate the value of sin x at x = 0.1.

A:

Q: Verify the identity sin 2t - tan t = tan t cos 2t.

A: Given:sin2t-tant=tant cos2tTrigonometry formula:sin2t=2sint costtant=sintcostcos2t=cos2t-sin2t

Q: Verify the identity. sin(x + y) – sin (x - y) = 2cos.xsiny

A: To verify the identity, sinx+y-sinx-y=2cosxsiny

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

A:

Q: Prove the identity. cosx sin (x+y) – sinx cos (x+y)= siny

A: In question We have given two identities and we'll prove it, (i). Cos(π + x) = - Cosx  (ii). Cosx…

Q: Verify. esc (x) [I-cos(2x)] = 2 sin (x) SC

A:

Q: sin-(x²)

A:

Q: If f(x) = 3 tan-'(3 sin(3x)), f'(æ) =

A: The given function f(x)=3tan-13 sin(3x)

Q: . Estimate the root of the expression, f (x) = x² – cos x, using: d. MOSS using xo = -1 with error…

A: As per the question we have to find the root of the equation : f(x) = x2 - cos(x) = 0 With tolerance…

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

A:

Q: Differentiate the function. f(x) = 5 sin2(x) − 8 cos2(x)

A: Given:

Q: ≤ Lºin( Verify that f(x) = sin() is an odd function and use that fact to show that 0 < sin(√√x) dx ≤…

A:

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

A:

Q: Find Maclaurin expression of f(x) = Cosh (x)

A:

Q: Prove the identity. + sin 3 cos x- cosx

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Q: find maclurin formula in the fourth degree for f(x)=tanx

A:

Q: Prove the identity. cosh(x) + sinh(x) - e

A: To prove the given identity we uses basic expression for sinh(x) and cosh(x).

Q: Express the product sin 4x cos x as a sum or difference.

A: Given: sin4xcosx

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

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

Q: Evaluate the definite integral. • */10 cos 5x sin(sin 5x) dx

A:

Q: Evaluate the definite integral. π/ 18 cos 9x sin(sin 9x) dx

A:

Q: Derive/Prove: sin 2x = 2 sin x cos x

A:

Q: 1. Which expression is equal to sec x tan z sin x using identities?

A: We can use simple trigonometric identities to solve the given equation.

Q: What is special about the functions ƒ(x) = sin-1 (1/ sqrt(x2 + 1))  and g(x) = tan-1 (1/x)?…

A: Given functions are

Q: evaluate the indefinate integral

A: Evaluate indefinite integral.