Evaluate: / [cos(x) – sin(x«) ]dr A cos(x) + sin(x) +C - cos(x) + sin(x) +C

Q: Cos x = Cos" x 1-

A: In this question we have to prove cosx=cos-1x.

Q: 1 - cos 2x if y = prove 1 + cos x y' = 2tanx.sec²x

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Q: 2 cos(4x) – 4x? – 2 - - 8. lim x→0 sin(2x) – x2 – 2x -

A: Topic = Limits

Q: On (-∞, ∞), three functions y₁(x) = cos 2x, y2(x) = sin² x, y3(x) = cos²x are linearly independent…

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Q: Verify the identity: sin(x - y)/(cos x cos y) + sin(y - z)/(cos y cos z) + sin(z - x)/ (cos z cos x…

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Q: Prove that cos(sinx) = /1 – x².

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Q: verify the results  sin 4x = 8 cos3 x sin x − 4 cos x sin x  tan2 x =1−cos 2x/1+cos 2x

A: To prove: sin 4x = 8 cos3 x sin x − 4 cos x sin x Proof: Since sin2x = 2sinxcosx sin2(2x) =…

Q: In(cos ax) ? limx-0 In(cos bx)

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Q: Prove sin 2x cot x (1 - cos 2x)

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Q: What values of x in the interval [0,2pi] satisfy 2 + 2cos(x) - sin2 (x) = 0

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Q: Prove the identity. cos(3x) − cos^3 x = − cos x sin^2 x − sin x sin(2x)

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Q: 2

A: Prove: cos²(x/2)=(sin²x)/(2-2cosx)

Q: Determine a root of f(x) = 2* +3 cos(x²)-2 with 10-3 accuracy.

A: Given :f(x)=2x+3cosx2-2

Q: * Prove: sin x = cos COS 2- 2cos x

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Q: Verify the identity. cos x = sin x sin 2x + cos x cos 2x

A: we have to verify the identity

Q: Verify the identity sec-1 x = cos-1(1/x), for x ≠ 0.

A: According to the question, we have to verify the identity sec-1x=cos-11x. As the above function is…

Q: verify cos(3x) = 4cos^3 (x) - 3cos(x)

A: We know that  cos(A+B)=cosAcosB-sinAsinB Therefore cos(3x)=cos(2x+x)=cos(2x)cos(x)-sin(2x)sin(x)

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: Prove that sin 5x + sin 3x/4 sin x cos^3 x - 4 sin^3 x cos x = 2 cos x

A: Given: sin5x+sin3x4sinxcos3x-4sin3xcosx

Q: If f(x) Files = Time left 0:5 sin²x and g(x) = 1 + cos²x, how are f'(x) and g'(x) related? Maximum…

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Q: Express 2 sinx- v2 cos x in the form of Rsin(x – a), w

A: Given expression is   2 sinx -2 cosx

Q: solve for allvalues of x in the interval 0 ≤x≤2π:  2-2sin^2 x+3 cosx=-1

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Q: Find sin(2x), cos(2x), and tan(2x) from the given tan(x) = -, cos(x) > 0 %3D sin(2x) = %3D cos(2x) =…

A: Given: tanx=-16,   cosx>0 sin2x can be calculated as, sin2x=2tanx1+tan2x          =2×-161+-162…

Q: x is in the interval [0, 2t) * sin2x - cos2x = 0 COS

A: Given: sin2x-cos2x=0; x∈[0,2π) We know that cos2A-sin2A=cos2A…

Q: Evaluate. de (sin(5x – 1)] cos(5æ – 1) 5 - sin(5æ – 1) 5 · cos(5æ – 1) • 5· cos(x)

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Q: 4. Prove that cos(sin¬1 x) = /1 – x².

A: cos(sin-1x)=1-x2⇒sin-1x=cos-1(1-x2)Let y=sin-1x                               (1) ⇒siny=x…

Q: 9. Prove. cos x sin x 1 - csc x %3D sec x

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

A: Given:

Q: provethat 2. 1- cosx +Sin'x

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Q: A force of F(x)=x2−cos(3x)+2, x is in meters, acts on an object. What is the work required to move…

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Q: Verify the identity: [sin 2x + (sin 3x + sin x)]/[cos 2x + (cos 3x + cos x)] = tan 2x

A: Consider the identity, sin2x+sin3x+sinxcos2x+cos3x+cosx=tan2x To apply the trigonometric identity,…

Q: Integrate x3 cos(x4)

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Q: x sin 2x sin COSX 8. Prove that: %3D 2x-7

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Q: 4) Verify. cos²(x)[1 C. – tan²(x)] = cos(2x)

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Q: prove that cos^2 x/2= tanx+sinx/ 2tan x

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Q: Evaluate the limit of x —> negative infinity. Cos (2x) / x+25

A: To find limx→ -∞ cos2xx+25

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

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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: 9. Prove: csc(x)-csc(x)cos² (x) = sin(x)

A: To prove: csc(x)-csc(x)cos2(x)=sin(x) Note that, sin2(x)+cos2(x)=1

Q: Suppose f(x) =cos ( 3x – 2). Evaluate: A -3sin(3x - 2)+C ® -sin(3x- 2) + C sin(3x – 2) +C 3sin( 3x –…

A: Given function f(x) = cos(3x-2)

Q: prove the identity sin^2xcos^2x+cos^(4)x=(1-sinx)(1+sinx)

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Q: when

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Q: (b) Verify that f(x) = 2 cos(x) sin(x). f(x) = sin(7x) + sin(8x) 7x + 7x = 2 sin 2 = 2 sin |co(-)

A: Let the function is  f(x)=sin(7x)+sin(8x)   Formula used: Sin(a)+sin(b)=2sina+b2cosa-b2

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: Verify that 2tan (x/2)= (sin2x+1-cos2)/(sin x(1+cos x)

A: Consider the given condition that,2tan (x/2) = (sin2x+1–cos2x)/(sin x(1+cos x)) … (1)Consider the…

Q: Verify the identity. sin 3x 1 = 2 cos x- %3D sec x 2 - sin 2x

A: Given: Verify the identity sin3xsin2x=2cosx-12secx for verifying given identity we solve left hand…