Find the total areas of the shaded regions in Exercises 49–64. 50. y 49. y = (1 – cos x) sin x y = xV4 – x² п 52. y = " (cos x)(sin(7 + ™sin x)) 51. -2 -1 х -2 y = 3(sin x)/1 + cos x 53. y 54. y = 1 y = cos²x TT 3 3 -4 sin?t y -4 2. 2. 3.

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Q: . Differentiate each function. a) y= cos'x b) y= sin(x³)

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Q: sinx + sinx CScx + 1 CScx - 1

A: Use following trigonometric identities  1. cscx = 1sinx 2.(csc2x - cot2x) =1

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A: ∫cos3xsinxdx

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Q: 2. Explain why arcsin(sin(0)) = 0 but arcsin(sin(807)) # 807

A: Concept  arcsin(sin x) = x   is true  only when x lie in the interval [-π/2 , π/2]

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Q: sin* x – cos* x = 1 x – cos? x

A:

Q: 8.) k(x)=-2 tan(2(x+)) Period = Increment =

A: Given function is: kx=-2tan2x+π8 Then the period of this function is 2π2=π. The increment is π8.

Q: (arctan o tan)' = 1 – pi k E z°(k +1/2)pi When differentiating on the Real line is this true?

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Q: V3 Tan" (-V3) Cos"(-1) 3. Sin 2 1. 2.

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Q: Using suitable method, show that 2 tan" (x+2) dx =- – In 2 .

A: We use integration by parts to find integral tan inverse x.

Q: (sin A)^4-(cos A)^4

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Q: 1 + sin x Differentiate y = x + cos x

A: As we know that: The Quotient rule: fg'=f'·g+g'·fg2 The Power rule: ddxxn=nxn-1 Given:…

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Q: how to find cos z using, cos^2x +cos^2 y+ cos^2 z=1     where x = 45deg  and y = 60deg

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Q: Evaluate * | (0² + 1) cos 0 d0. e2sine + 20cose – sine + c 02sine – 20cos0 – sine + c Option 1…

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Q: sin-'x - cos-1x = " Find the value of x

A: Given that sin-1 (x)-cos-1 (x)=π6, Our Aim is to find the value of x=?

Q: :: Evaluate: S sin 2x sin x dx 1/3 sin'x + c 1/3 sin'x +c 2/3 sin'x + c d. 2/3 sin'x +c a. с. b.

A: Given: ∫sin(2x)sin(x)dxWe know that sin(2x) =2sin(x)cos(x)Then…