cos(: sin@)]=[- sin(esin@)]. * (b) (i) Show that - cose dt

Q: cOs x tan x 28) lim sin 3x 29) lim x→0 2x x3 + 2x2 + x 30) lim x→-1 x4 + x3 + 2x + 2 x3 – 2x2 + 4x –…

A:

Q: (g) tan sec2 dx (c) sin“(3x) cos (3x) dx CoS'

A: Given: I1=∫sin43xcos33xdx, I2=∫tan4x2sec2x2dx

Q: 1 sec- x = cos

A: Given, sec-1x=cos-11x   Check it is True or False:

Q: 6. cos x(csc x secx) secx) cotx

A:

Q: csc squared x/2 = 2/1-cosx verify with steps

A: To Verify:

Q: (1+cos3x)² -dx sin23x

A:

Q: 2-sec2x: COS2X = COS X

A: Given query is to verify the identity

Q: 10) lim TT X-- sinx-cosx - TT X- 4

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Q: Find the period and amplitude of the function. 2n y=-4 sin x- 3 Give the exact values, not decimal…

A: If y=AsinBx is a function then its amplitude is A and its period is 2πB.   The given function is…

Q: cos(x) / 16 - sin2(x) dx

A:

Q: 43. Use the identity cos 2x = cos x cos x - sin x sin x to find the derivative of cos 2.x. Express…

A: cos2x=cosxcosx-sinxsinx find the derivative of cos2x So here use product rule and then find…

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

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Q: symbolnc cos(6x) cos(11x) dx = cos(11) sin(6x) + C ncorrect

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Q: Find sin 4.x cos 8x dx.

A:

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

A: To prove the identity

Q: -sin^2(x)=cos(2x) from [-pi, pi]

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Q: Find ∫sin3 x cos4 x dx.

A:

Q: Since the functions y cos(x) and y -1 = cos are inverse functions, explain why COS (cos(-)) is not…

A: use the range of arc cosx to find the values

Q: sin(2x) cos(2x) dx 1+ cos(4x)

A: The complex form of integral can be converted to simple integral using integration by substitution…

Q: 21. cos x cos 2x + sin x sin 2x

A:

Q: cos(4x) cos(2x) sin(4x) sec(2x) 12. Verify: - sin(2x)

A: cos(2x ) =cos2(x)-sin2(x) = 2cos2(x)-1 =1-2sin2(x) sin(2x) = 2sin(x) cos(x)

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

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Q: sin(-4x) cos 3x dx 1. 3

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Q: 5. y = -2 cos x - - Amplitude: Phase Shift: Period:

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Q: tan x dx sec x+4 cosx 5.

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Q: sin2x -dp- cos x+cos*x-2cos?x

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Q: sinh4x cosh 4x dx can best be evaluated by General Power Formula. A True False

A:

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

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Q: | sinh54x cosh 4x dx can best be evaluated by General Power Formula. A True В False

A: The given integral is ∫sinh54xcosh4x dx. We have to check whether the given integral can be…

Q: Cos(5x) cos(2x) + sin(5x) sin(2x)

A: Given: Cos(5x) cos(2x) + sin(5x) sin(2x)

Q: Integrate cosx cos (x-a)

A:

Q: 1+ cos x sin x 7. Verify: ¹ 11 csc x + cotx

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Q: cos^2x+sin^2x/cos^2x=

A:

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

A:

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: sin 5x cos 3x dx

A:

Q: 3 cos xdx 1-sinx

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Q: sin x and coS x are periodic functions with period Tt. True False

A: Given statement is "sinx and cosx are periodic functions with period π."

Q: Find cos(2x) Given that sinx= 4/5 and 0&lt;x≤ pi/2

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Q: 1- cos 4x 9. sec2 2x – 1 = 1+ cos 4x

A:

Q: 3. When e is in standard position and its terminal side passes through the point (4, -2) Find the…

A: Given: θ is in standard position and its terminal side passes through point (4,-2)

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: If siny=x^2 Then find the value of cos2y

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Q: . Evaluate cos 3x sin² 3x dx

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Q: Evaluate ax xm-1 sin bx dx in terms of Gamma function. -ax

A: We use the special results of Gamma function to solve this problem as in next step.

Q: If csc 0 = 2, calculate an e sec () sin² 0 exactly.

A: We use cosec x=1/sinx and tanx=sinx/cosx,secx=1/cosx. See 2nd step.

Q: If sinx = siny = a and cosx = cosy = b,then cos(x-y) is

A: