sin x+ tan x sin (2x) 5. Determine the non-permissible values of the identity 1+ cos x 2 cos x Cos3x tO cos x # -I x 7 TT

Q: b. cos ( I1/2 -x) c. cos(x+ II/2) d. tan(x+ II/2) e. tan( II/2 -x) a. sin ( I1/2 -x) 16. sin x 15.…

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Q: Find  (f −1)'(a). f(x) = 3x3 + 3 sin x + 3 cos x,    a = 3

A:

Q: sin? x 1- 1-cos x =-COS X

A: Here we have to use the basic trigonometric identity sin2θ+cos2θ =1 and we know that  a2-b2=…

Q: h(x) = tan x - tan-x h(x) = 3 sec-1x h(x) = 14 cot x + 12 cos-x h(x) = (3x? + x - 1) csc-x %3D

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

Q: (÷++) + co« (5 - ). cos 3 x ) is equivalent to O cos 2x cos x O sin x cos x

A:

Q: Evaluate the integral. π/2 9 sin2(x) cos2(x) dx   0

A: Consider the definite integral: ∫0π29sin2xcos2xdx…

Q: Verify the identity:

A: Our Aim is to verify the identity given below:-sin 3π2-x=-cos (x)  -(i)

Q: sin 2x 10. Simplify 1-cos x (a) 2cot x (1+ cos x) (b) sin 2x (1 + cos x) (c) sin 2x (d) – 2 tan x (1…

A:

Q: sin'x cos x dx (1– sinx)2(1+ sinx)? Evaluate: sin 8x

A: To evaluate: ∫sin7xcos5x1-sinx21+sinx2dx

Q: Establish the identity. sin x- sin y x+y cot 2 COS X- COs y Which of the choices shows the key steps…

A: To prove the following trignometric identity:

Q: (a) Find S(tan x)dx (b) Evaluate i sin 3x cos 3x dx d (c) Find (2x sin 2x + cos 2x) and hence…

A: a) ∫tan2πx dxb) ∫π9π6sin3x cos3x dxc) ddx2xsin2x+cos2x and ∫0π4x cos2xdx

Q: 11. y = coS x COS X -2 tan x 12. y = x? sin x tan x 13. у %3D 1 14. y = --3 sin x 15. y = x cot x

A:

Q: Calculating derivatives Find dy>dx for the followingfunctions.

A: Since you have posted a multiple sub-parts ,we solve first 3 subparts for you .To get the remaining…

Q: 1/sin(x)/cos (x)+cos (x)/1+sin(x)=4 Prove

A: For x= pi/3

Q: sin x(cos x-1) 8. Prove sin(n -x) – tan(t + x) | COSX

A:

Q: 65. 3 sin x = cos x 67. cosx- sin²x = 1 69. 2 cosx- 3 sin x- 3 = 70. 2 sin?x - cos x - 1 = C

A: 67. cos2x - sin2x =1 1 - 2sin²x = 1 Cos2x =1 2x = cos-(1) 2x = 0, 2π , 4π ..... x = 0,π,2π  So…

Q: Derive/Prove: sin 2x = 2sin xcos x Useful Formula: cos 2x = cos?x-sin? x a. = 2 cos x-1 =1-2sin x…

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Q: Using an appropriate substitution, cos x-sin x the integral 3. dx equals: 0 cosx+sin x O none of…

A:

Q: 1+sin x sin x <x<0 6 -- If f(x) = {b , x = 0 is continuous at x = 0, find the values of a and b. tan…

A:

Q: 20. cos x 3 cos x -V2 cos x csc x; xe[0,2n]

A:

Q: cos(x1)=-1/3 sin(x2)=2/3 find 1. sin(x1+x2) 2. cos(x1+x2) 3.sin(x1-x2) 4.cos(x1-x2)

A:

Q: Choosing between A B or C HW 12

A: We know that,

Q: Verify the identity. cos(e) sin(0) - csc(0) 1- sin(0) cos(0) - cot(0) sin(e) – sin(0) sin(e) –…

A:

Q: [cos x - sin x 0] cos x 1] 5. If f(x) = | sin x 0|, show that f (a)f(b) = f(a + b).

A: f(x)=cosx-sinx0sinxcosx0001

Q: 1-T= 3- Z= +cos(y)tan ( √x-b cos (n) 2-sin²(n) 2-B=sin(x) sec(x)/cscf(x) 4-(w+n)²(a+) x-3

A:

Q: 1- cos e sin 0 sin 0 1- cos 0 23.

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

A: In this question we will use basic of calculus i.e concept of integration. We will simply use the…

Q: 3x2 sin(x³) Select one: а. In/tan x3 + cot x³| + c b. -In csc x3 + cot x³| +c С. с. In|sec x3 +tan…

A:

Q: sin(5x) dx 2+сos(5x) اخترأحد الخيارات х + tan(5x) + с.ао —In | 2 + сos(5ӕ) | +с.Ь 1 +c.c 2+сos(5ӕ)…

A: Since , in the given integration problem we have derivative of denominator in numerator so we will…

Q: - sin sin -y = sin (x+y) Prove that cos Xcos 4 -y 4 -x sin 4 X - 4

A:

Q: Prove the pollowing identity.. (sin x t cos L cas x)- sin 2X-CoS T Sin'x + Cosx

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Q: tan(x) dx cos4(x) tan'(x) A [7tan²(x) +9] + C 36 1 ℗tan'(x) + tan³(x) + C C D sin²(x)sec³(x)…

A:

Q: sin x= 6/7, cos > 0, sin y = -1/5, and cos y < 0 How do I find sin(x + y), cos(x + y), and tan(x +…

A: Given that  sinx=67, cosx&gt;0,siny=-15and cosy&lt;0. We know that…

Q: sin x 16. Evaluate f dx cos²x a. tan x sec x + C b. sec x c. sec?x d. tan x

A: Using substitution method Let cosx =t

Q: Simplify (cos x- sin x)(cos x+ sin x). sin x cos x O 2 cos x-1 2 cos x+1

A: Given: cosx-sinxcosx+sinx

Q: 1. sin x sin 2x + cos x cos 2x = COS X

A:

Q: 2 – 2 cos 2x sin x sin x cos x sin 2r 1- sin r 1+ sin x

A: Trigonometric ratios

Q: tan (x) J Cos cos“(x) 하an7(x) + 늑tan®(w) +C O tan'(x)7tan?(x) +9]+ C tan7(x) 36 O sin…

A: Here we have to integrate the given function.

Q: lim E(cos (27x;))Ar over [0,5] COS i=1

A: The definite integral is defined as  ∫abf(x)dx=limn→∞∑i=1nfxi*ΔxWhere, Δx=b-an, xi*=a+iΔx The…

Q: Verify the identity. sin³(x) + cos³(x) = 1 – sin(x) cos(x) sin(x) + cos(x) sin3(x) + cos³(x) sin(x)…

A: we know that  a3+b3=a+ba2-ab+b2

Q: Prove the identity. sin(n-x)сos(n+x)tan(2π − x) T 3π 3π sec+ x)csc(³7-x)cot (³7 + x) = sin^x - sin²x

A: I have appended the formula used in the solution part of the question

Q: X+1 1-x Select one: a. sin-1(x)-V1-x² +c www. O b. sec-(x)-V1-x? + c C. tan (x)-V1-x2 + C d. cos x)…

A:

Q: 4 sin x cos x + 2 sin x - 2 cos x - 1 = 0

A: first factorize the given equation and than split two product equation  detailed solution is given…

Q: x(1+x?) sin x+ cos x + x² cos x – x cos x (1+ x³)% = (1+x?)?[cos x– x(1+x?)sin x]

A: We want to prove that both equation are equal.

Q: 2x² sin (x²)dx = V(1-x*) Select one: a. - sin-(x²) cos(sin(x²)) + x² + C b. - cot-(x?) sec(sin-(x²))…

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Q: 1+2 sin x cos x 1-2 cos2 x sin x+cos x (d). sin x-coS x | |

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Q: 3+(e*+3) sin x %3D tan(x³)-x

A: y=6x3+(ex+3)sinxtan(x3)-x

Q: tanº(x) cos“(x) O sin'(x)sec°(x)[7sin?(x) + 9cos²(x)] + C 63 tanʼ(x) [7tan²(x) + 9]+c 36

A: The properties to be used for solving the integral are: a) 1/cos4(x)=sec4(x) b) d(tanx)dx=sec2x c)…

Q: 1- sin(x) A cos(x) +x+C COS 1+ sin(x) B -x+C cos (x): cos(x) -+C cos(x) – x 2cos(x) D 1+ sin(x)

A: