2. 1-tan x w) cos2x 1+tan x |3|

Q: Prove that 1-x ', V 2 1+x cos'x = 2 sin 2cos 2 COS 1 -1

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Q: 5- Prove that a) tan x (csc x – sin x) = cos x b) 1+ sec?x sin?x = sec?x

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Q: -1 3. Show that sin-¹x = tan X √1-x² if |x| < 1.

A: Introduction: When there are trigonometric functions present in an expression or equation,…

Q: 2 Using the relation 2 (1 cosx) x, V x € (0, - · 4)

A: A relation is given by, 21-cosx &lt; x2, where x≠0. The objective is to use the given relation to…

Q: Show that 2 sin 0 + sin 20 sin 0 1- cos 20 1 cos e Prove that (G) 1 T 1 tan-1 + sin V5 3. where…

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Q: 48. tan x = -0,974; con 5 < x < a a. sen x d. sec x b. cos x e. csc x) c. cot x

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Q: Q4: Prove that: (1- sin x)(1 + cscx) = cos x* cot x %3D

A: To Prove1−sinx1+cscx=cosx×cotx

Q: Prove that 1- cos 2x = tan x sin 2x. %3D

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: (b)Prove that if f (x) = In (cosx), then f'(x) = -tanx.

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Q: 12 Prove that sin 80 cos 0-sin 60 cos 30 a. = tan 20 cos 20 cos 0- sin 30 sin 40

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Q: b) sin 3x 3 sin x – 4sin3 x [Hint: sin 3x sin(2x + x)] Prove

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Q: Osl 2. 2Sin x- CosX+1 = 3 tan x 2 Cos?x

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Q: If tan then 1– 2 1+ z2 COS X 8 |N

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Q: 1 1 Express in terms of csc(x) 1+ cos x 1- cos x

A: Given:     To determine: The given expression in terms of cscx

Q: 1 1 Prove -2 secx tan x 1+ sin x 1- sin x

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Q: - IF z = tan2 -1 y Show that x- ây

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Q: 3. Give upper and lower estimates (in terms of n alone) for sin nb COs na + valid for all a, b; show…

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Q: 2c. Show that * (5 - ) 4 sin z - cos 2r + 3 -8 cos for every r.

A: To prove: 4sinx-cos2x+3 = 8cos4π4-x2 We know that cosx-y  = cosxcosy+sinxsiny and cos2x= 1-2sin2x

Q: 2. * 1 Add File 3. * 1 y = tan x + =tan³x 3 4. * y = = cos x 1 Add File y 1 cos³x 3 1 cosx

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Q: Show that (tan−1 x)'= cos2(tan−1 x) and then use Figure to prove that (tan−1 x)' = (x2 + 1) −1.

A: The objective is to show that:  tan-1x'=cos2tan-1x.   Use the formula: ddxf-1x=1f'f-1x. Here,…

Q: D,(6 tan x) 6 sec² x sec² x (c) D,(In |6 tan x|) %3D 6 tan x 6 tan x tan x

A: Consider the given function as Dxln6tanx

Q: Let S(x) 9 sin x + 9 cos x "(x) 3= r(-)-

A: A function is given as fx=9sinx+9cosx. The objective is to find the first derivative f'x of the…

Q: 3. Prove the identity : sin(x- y) tanx - tany cosxcosy

A: The given identity is, tanx-tany=sinx-ycosxcosy The identity will be true if the left-hand term will…

Q: If 1, = | x" sin x dx, prove that 1, = nx"-! evaluate -1,. sin x- x" cosx– n(n-1)I, 2. Hence, = NX…

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Q: 5л Compute the exact value of tan ( + 4 ). 6.

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Q: Q1// prove one only: tan²x-1 tan²x+1 = 1-2cos²x

A: Topic = Trigonometry

Q: a. Show that y = tan u increases on every open interval in its domain. b. If the conclusion in part…

A: y=tanu Differentiating with respect to u, we get dydu=sec2u Now clearly, sec2u≥0 for every value of…

Q: 1 Prove that sin x tan x = cos x. cosx

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Q: 4.) Prove: sin 2x a) 2cos? x = tan x b) sin 3x = 3 sin x – 4sin3 x [Hint: sin 3x = sin(2x + x)] -

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Q: 5. Prove the following identity 1- cos X tan2 2 %3D 1+ cos x

A: The solution is :

Q: Prove the identity 1+ tanz 1- tanz = tan (r

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Q: HW/ Prove that: (1) 1-tanif x sechx

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Q: 1+cos 4x Express without double angles. sin 4x O (cot a + tan x) O ÷(cos x 글 (cos sin x) - O (cot a…

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Q: 1) Prove the following: [tan (x) + 1]|cos*(x) – 1] = -tan²(x) %3D

A: Since we are supposed to solve only one problem as per policy, I am solving question no 1 here. For…

Q: (b) Can we use the IVT to conclude that f (x) = tan(x) equals 0 for some c in (0, 1)? %3D

A: We can answer first question among which you asked as per the honor policy. please resubmit the…

Q: find maclurin formula in the fourth degree for f(x)=tanx

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Q: VERIFY THE IDENTITIES

A: To verify

Q: Prove that 1+ cos x + V1-cos x X +,0<x<" 4 tan %3D 1+ cos x -V1- cos x 2

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Q: n x)(\sec x+\tan x) \equiv \cos x, \quad nathbb{Z} .

A: (a)  To prove that: (1-sinx)secx+tanx≡cosx

Q: Prove cos* x – sin* x =1–2sin² x

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Q: 3) Prove that b) tan- (*)} = sechx

A: Evaluate the derivative of the given function as follows. ddxtan-1ex=11+ex2ddxex…

Q: 44. sec x = 1,642; con 0 <x <5 a. sen x d. cot x b. cos x csc x е. c. tan x

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Q: 4. Prove that tan x – cos x = sec x – cosʻ x - x- cos cos x – 1. :

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Q: Prove that? 2tanX tan 2X %3D 2 1- tan x

A: Given : 2tanx1-tan2x = tan2x

Q: 7. Verify the identities: tan x tan x tan20 1-cos e a) 1+sec x = 2 csc x b) sec 0+1 %D 1-sec x cos e

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Q: Let f(x) = cos^-1(√x). Then f′′(x) is equal to?

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Q: Q3:A| Prove that:- cos x 1) 1+sin x 1+sin x = 2 sec x cos x tan? x 2) tan? x+1 = sin x

A: topic - trigonometric identities

Q: (1+cos(x))(1-cos(x))=1/2sin(2x)tan(x)

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Q: 5. Prove the following Identity: sin(2x) 1+ cos(2x) tan(x)

A: Use the following identities to prove  the given  identity. sin²x+cos²x=1 cos(2x)=cos²x-sin²x

Q: (6) Given that In= tan" x dx, show that, for n 2 2. %3D In- In-2 = %3D n- 1

A: I think given question is slightly wrong. According to me the required proof should be…