tan x 4. a) Evaluate dx. In (cos x) b) Evaluatef e4*x3 dx.

Q: (a) Evaluate| cos (4x) -dx. (1+ 2sin ( n(4x)*

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Q: 2. Prove the following identity: sin (x+y)sin (x-y)=cos² y-cos²x X =COS - COS¯ x X.

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Q: Suppose = cos 4- Evaluate: |dx A - 3sin sin x-4+ C © -)+c -x- 3 3sin

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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: (b) Let f(x) = sin (cos-1 (sin(cos-vx))).B f'(1) = using chain rule, show that %3D

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Q: b) cos(-z)=?

A: In the question we have to find the angle of cosine which is lying in third quadrant as cosine is…

Q: Determine whether the statement (d/dx) [arctan(tan x)] = 1 for all x in the domain. is true or…

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Q: 2- tan x dx Can be calculated if n: A. n= T/4 В. п/2 С.-п/2.

A: ∫0ntanxdx

Q: tan(e-2*) In(cos(e-2*)) dx e 2x

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Q: CianXtl) 2 tan x 8. Prove the identity: sin 2x = 1+ tan x L.S. es

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Q: 5. Verify the identity: sin(x- y)cos y+cos(x– y)sin y = sin x

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

Q: 3. e<4TI. 2. ind 3. where when tan e = -

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Q: If f cos xdx = A +B sin x + Csin²x+ Dsin³x+ Esin*x+ Fsin5x, what is , 2 ) and ( - 2,5). the value of…

A: Given: ∫cos5xdx=A+Bsinx+Csin2x+Dsin3x+Esin4x+Fsin5x.

Q: 2 cos" (x)–sin°(z)+1 cos(x) 3 cos(x) 10. Verify the following identity, justifying each step.

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Q: 4. Verify the identity sin(z+y) %3D COB E COS y tan z+ tan y

A: “Since you have posted multiple questions, we will solve first question for you. To get remaining…

Q: Prove the identity cos(x+y)cos y +sin(x+ y)siny =cos x

A: We have to prove the identity                              cosx+ycosy+sinx+ysiny=cosx

Q: Prove that d/dx tan(x) = sec^2(x).

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Q: Establish the identity. sin x+ sin y X+y = tan COS X+ COs y 2.

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Q: 8. Convert all expressions in (a-<) to a form A (x)+ B (x) dxteNote that A and B will vary from <ase…

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Q: (14) Prove the following identity cos(x + y) + cos(x - y) = 2 cos(x) cos(y). Make sure you show all…

A: We have to prove the given identity- cos(x + y )+cos(x - y) =2cos(x) cos(y).

Q: Using (11) and (12): 1 dx 1+ cos x tan +c

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Q: Sin 45" Tanko' t 30° Cas 135¢ Cos 135 7 Tan I50 cos 120°

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Q: bx + c Given tan 3 - In(x2 - 8x + 25) + 1 -dx %3D x2 - 8x + 25

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Q: 3. Prove that the identity is true. sin*t - costt tan-t– 1 cos't

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

Q: Find дх (дхду) 6,e at the point(7,), where g(x,y) = cos(y) [sen(x) + xy].

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Q: Another form of sec x dx cos x 1- sin²x b. Use the identity in part (a) to verify that 1. |1 + sin…

A: a) we have to verify the identity sec(x)=cos(x)1-sin2(x)Consider, RHS=cos(x)1-sin2(x)we…

Q: (B) The evaluation of f- -dx is (x*+3x2 +1)[tan-( In|tan"+5| + e -In tan-( +c (i) (ii) (iii) None of…

A: No antiderivative could be found within the given time limit, or all supported integration methods…

Q: is cos x = 1/sec x an identity

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Q: Establish each identity given in attachment.

A: To establish the identity: lntanθ=lnsinθ-lncosθ Solution: We know that, tanθ=sinθcosθ Property of…

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: * tan(x) dx Evaluate: A 1 In In (2) In (3)

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Q: Evaluate si (z* - tan(z) cos(z) ) dx 2-1

A: To find the integral: ∫11x2-tanxcosxx3-1dx

Q: A/ 10 Evaluate 4/1+ cos 10x dx. A/ 10 4/1+ cos 10x dx =

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Q: Evaluate in x cos x dx. .3 I COS" T

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Q: tan e lim is 3 5 sin e O a. 1 5 O b. 5 Oc -1 O d. o

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Q: x=cos¬! 1 prove that sec" X= cos

A: Given sec-1x=cos-11x

Q: If (tan r + sec x)² A + sin x В - sin x then A B =

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Q: Consider (D² + 1)y= se = sec x . If y, = f cos x + g sin x, what is f and g ? A = In cos x|, g = x f…

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Q: Evaluate sin z -dx /4 - coS I

A: Use the substitution method and first simplify the integration than integrate.

Q: х Given that t= tan , show that: 1-1? 2t d) sin x = 1+t? e) cosx = 1+1? 2t f) tanx = 1-?

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Q: Prove that 55 sin x² dx - 5 cos x² dx = 1/2 √

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Q: Obtain the reduction formula for ∫tan"x dx, and hence evaluate ∫ tan5x dx.

A: ∫tannx dx=∫tann-2x·tan2x dx=∫tann-2xsec2x-1 dx      ∵sec2x-tan2x=1=∫tann-2x sec2x-tann-2x…

Q: Is this: sin x cos y- cos x sin y/ cos x sin y reciprocal quotient pythagoreom  algebra

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Q: Evaluate f sin° (x) cos“ (x)dx Select one: cos (x) cos" (x) + C 5 7

A: The given integral is ∫sin3xcos4x dx

Q: tan y = In 2 + e"

A: Given : tany = ln2x2+e-xy

Q: tan(0) Insec(0) de (A (Insec(0))²+C (Insin(0))²+C 2 - (Intan(e)) ²+C D -Incos (0) + C 2

A: We have to evaluate the integral ∫tanθlnsecθdθ For this, we shall use the method of substitution.

Q: O cos y (cos x + 1)

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Q: a/2 -6 cos (x) dx

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Q: Prove the identity. cosh?x (cosh(2x) + 1) 2

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