1. y = 3 sin x – 4 cos x 2. y = x³ tan x 3. f(x) = cos x 1+sinx 4. y = csc x cot x f(x) cin?

Q: Siven cos x E and π x<. 5 ", find tan(2x) %3D

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Q: (sech°x)/1+ sin? if y = dx dy Find tanh°x

A: Given:-       To find:- dy/dx

Q: y'tan x sin 2y = sin² x + cos² y.

A: We need to solve y' tanx sin2y=sin2x+cos2y This can be written as: y' tanx…

Q: 플) - cos X = sin x 2.

A: cos(x-π2)=sin x

Q: Evaluate the integrals

A: We have to evaluate the given integrals .

Q: · y = sin(cos 3x) – sin x cos 3x

A: Given : Y = sin(cos3x) - sinx.cos3x Let's differentiate:

Q: 4. Evaluate sin (x) cos°(x)dx

A: To evaluate the integral

Q: = 0 If 2 sin x cos x + V2 cos x = 0. 0, then %3D %3D or

A: 2sin x cos x +2cos x=0

Q: -1 We can conclude from the derivative of sin-1(x)and cos-1(x) that sin-(x) + cos¯(x) is constant.…

A: Explanation: find the derivative of sin-1x &amp; cos-1x

Q: If y=a cos(sinx)+b sin (sin x) then y"+(tan x)y'+cos2x=0

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Q: 2. (a) Find the tangent line approximation to sin(x) near r 0. (b) Is the tangent line approximation…

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Q: 1 Differentiate y = tan 8x + cos ,x

A: Using differentiation rule,

Q: 2 + sin x Differentiate Y x + cos

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Q: 1. y= sin 2x 2. y=2 tan.x 3. y= cot 3x

A: I have provided solutions in step2. because of our guidelines, we can answer only 3 questions so…

Q: 15 cos(x) + 4 sec (x)dx

A: 1) I=∫15 cosx+4 sec2xdx =15∫cosx dx+4∫sec2x dx =15 sinx+4 tanx+c   (c- constant if integration)

Q: Verify the identity: (sin x - sin y)/(cos x - cos y) = -cot (x+y)/2

A: sinx-sinycosx-cosy=2cosx+y2sinx-y2-2sinx+y2sinx-y2=-cosx+y2sinx+y2=-cotx+y2…

Q: y= sin(x + 4) cos (x - 4) y= sec 4x + tan 4x y= Arctan

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: find the value of so that ky"=-1 at y=. 6. For cos x- sin y=-

A: On solving this by doing differentiation implicitly we get

Q: Show that x² + 1 cos{arctan[sin(arccot x)]} = V x² + 2

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Q: 11) (y)* = (In tanx)(x*)(sin x)* %3D

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Q: 11) (/y)* = (In tanx)(x*)(sin x)* %3D

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Q: Differentiate.  y =cos x /(1 - sin x)

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Q: (2 cos 2x+ 3 sin 2.x) 7. evaluated at x = 1 rad

A: Given query is to find the value of the expression at x = 1.

Q: et sin x – x lim x → 0 3 cos x – 3 - (Us

A: Given: limx→0exsinx-x3cosx-3   We know that; The Product rule: f·g'=f'·g+f·g'

Q: 7.) cot 2x dx 8. (sin x + x) dx 9. J (cos x sin2x) dx

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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:…

Q: Show that the two formulas are equivalent                                                      ∫tan…

A: To show that ∫tanx dx=-lncosx+C and ∫tanx dx=lnsecx+C both formula are equivalent. We know that…

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: Second-order derivatives Find y″ for the following functions.

A: "Since you asked multiple questions, we will solve the first question for you. If you want any…

Q: 4,5in3x =sinx S Sinx(sin?x-\= sin?x. Sinx(sinx-1). COS X tank (sin zx - COS tan-o TT

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Q: xy2-cos x sin x y' = ху?-со -cOs x sin У(1-x?)

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Q: 9. y = -sin (3x) 10. y = tan (x - 60) 11. y = cos (x + 30) 12. y = 3 cos (2x)

A: In both cases there is translation of graph.

Q: 21. y = csc 2x 22. y = tan 2 Vx* + 1 x tan x 24. y 23. у x? + 1 1 + sin? x

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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: Given that | sec (x) dx = tan(x) + A and tan(x) dx = ln | sec(x)| + A. Show that O sec2(0) d0 = 0…

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Q: 4 cos °x sin x dx 3x sin: 1/3

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Q: 2. If sin x cos x + sin 2x =1 what are the values of x

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Q: y = Arccot (cosx ) ; y' ' O sin x/ (1+ sin*2 (x) ) ) - sin x / (1+ sin^2 (x) ) ) sin x/ sqrt (1-…

A: Given y=cot-1cosx We will find y'that is the derivative of y. Chain Rule: If y=fgx, then y'=f'gx·g'x

Q: dx 2 sin x - cOS X |tan+ 2 + V5| In 5 tan; + 2– V5 |tan+2-V5 + C + 2+ V5 2. + C In Option 1 O Option…

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Q: If x is measured in degrees and f(x) = cosx, then d f(x) = − sinx

A: To write that it is true or not.

Q: 7/3 In(tan x) dx T/4 sin x cos x dx

A: It is simple substitute method of integration

Q: 16. S cot xdx /1 + In sin x

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Q: Show that n/2 sin x dx sin x + coS X %3D 4

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Q: 3 5. cos x dx > 6. sin x cos x dx =

A: According to the trigonometric ratio:  sin2x + cos2x = 1 Integration of cos x is sin x.

Q: If y = sin (sin x) show that y"+ (tan x)y +y cos x = 0.

A: Answer

Q: 4x 3x + cos (2x² + 1) tan? x) x (1+ sin² dx

A: Here We have to evaluate;  a) ∫4x3x+cos(2x2+1)dx b) ∫tan2x(1+sin2x)cos2xdx

Q: (11). - cos?(2y) sin? (x), y(등) =0 Workings y= tan '(z - 글sin 2v) +

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Q: at y = ". For cos x – sin y=-, find the value of so that ky'"=-1 at y="

A:

Q: 04.) Show that y = (sin x +cos x) sec x = sec² x

A: Given inequality does not equal. See the attachment