(a) Prove that, if n > 1 is a natural number, then tan"-(r) tan"-2(r) dr. n-: tan" (r) dr n - 1 Use this formula to evaluate tan (r) dr.

Q: Show that 2 tan(A) tan(2A) = 1- (tan(A))? tan(2A) =

A: We have to prove

Q: 10. Prove the following identity: tan² x+1 1 %3D tan² x-1 sin² x-cos² x

A: Topic - trigonometry

Q: Which of the following is equivalent to secβ(tan2β+1) for all values of β for which secβ(tan2β+1) is…

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Q: .2 -If tan -1 = 0, then prove that x2 sin 2 a. %3D

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Q: Prove the identity. 3 sin(x - y) 3 tan x - 3 tan y = cos y cos x

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Q: Prove the identities. 2 tan x (a) tan 0 sin 0 + cos 0 = sec 0 (b) 1 + tan?x sin 2x

A: To Determine: prove the identities  Given: we have  tanθ sinθ+cosθ=secθ Explanation: we have an…

Q: .2 -1 -If tan - a, then prove that x2 sin 2 a. %3D

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Q: (a) Prove that, if n> 1 is a natural number. then tan"-(r) /- tan" (r) dr. tan" (r) dr n- 1 Use this…

A: Prove that ∫tannxdx=tann−1xn−1−∫tann−2xdx

Q: 1. Verify the following identities. sec4 x - tan4 x 2 sec2 x - 1

A: We have given the identity

Q: V1+x2-V1-x² -1 If tan 1+x +V1-x² =a, then prove that x2= sin 2 a. %3D

A: Introduction :

Q: 10) Find the exact value of: tan +tan B tan (A+B)= -tan A tan B tan + tan 1-tan tan 5T TC 4 12 5TT…

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Q: Prove the following identities  (1+tan A tan B)2+(tan A-tan B)2=sec2A sec2 B

A: According to the standard relations between trigonometric ratios, we have: sec2(x)=1+tan2(x)

Q: (a) | Show that tan- z = in() = n 1, і —z i + z -In i - z -In z +i %3D | - (b) values of tan-(2 +…

A: This is related to Complex Analysis

Q: Prove the identity 1/Cos X - 1/Sec X = Tan X * Sin X

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Q: Prove: 1. tan (A/2) = - cos A 1 + cos A sin A 1+ cos A 2. tan (A/2) = ±

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Q: 23т Find the exact value of tan ( 23) 6 V3 O Undefined O -V3 V3 O -1 O V3 O 1

A: Use tan (180+thetha) formula

Q: Verify the identity:(1 - tan2 x)/(1 + tan2 x)= cos 2x

A: Given 1-tan2x1+tan2x=cos2x

Q: Verify the identity: (tan2 θ + 1)(cos2 θ + 1) = tan2 θ + 2

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Q: Prove the identity. 1+ tan 0 1 + cot0 = 0 1- cote %3D 1- tan 0

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Q: 1. prove that tan A sin 2A = 2sin2A %3D

A: Please refer the attached image for complete solution. THANK YOU.

Q: (a) Prove that, ifn>1 is a natural number, then tan"(r) dr tan-(r) tan" (4) dr. R-1 Use this formula…

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Q: (a) (i) Use de Moivre's theorem to express cos 40 and sin 40 in terms of cos 0 and sin 0. 4 tan3 0 4…

A: Expand the expression:  x+iy4=x4+4ix3y-6x2y2-4ixy3+y4=x4-6x2y2+y4+4x3y-4xy3i Set x=cosθ and y=sinθ…

Q: 2. Verify the following identities (a) sec e - tan@ =sec 0+tan6 sec 8+tan 6

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

A: Topic = Trigonometry

Q: Prove that ? 2tan X tan 2X 2 1-tan x

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Q: 6. Do EITHER part (a) OR part (b) OR part (c). (a) Prove that, if n>1 is a natural number, then…

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

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Q: m -1 :If tan A = n tan B and sin A = m sin B, prove that cos A = n -1

A: Given that  tan A=n tan B sin Acos A=nsin Bcos B ................equation 1 also given that  sin A=m…

Q: prove that sin(45° + A) sin(45° - A) = 1/2cos2A

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Q: Show that 2 tan(A) tan(2A) 1- (tan(A))? tan(2A) = ||

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Q: Prove the identity. tan(2pi-x) = -tanx

A: Formula used:tan(A-B)=tanA-tanB1+tanA.tanB

Q: Establish the identity tan (3r +0) = tan 0. Which of the following four statements establishes the…

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Q: 1-To find the smallest positive root of tan x-x=0 which of the following re-arrangement is…

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Q: Prove the identity. V3 + tan(x) tan(x + ) - 1- V3 tan(x)

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Q: tan" xdx = tan п-1

A: The integral is given : ∫tanndx=tann-1xn-1-∫tann-2xdx Apply the  reduction formula for the given…

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: 7. Prove the identity. 1-cos 20 tan 0 %3D sin 20

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Q: 1. Use an identity to find the value of tan (0 – 180°). O - tan 0 O-1 O 1 O tan 8

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Q: Prove the identity. tan(x +) V3 + tan(x) 1-V3 tan(x) tan(x) + tan= tan(x + ) V3 + tan(x) 1- V3…

A: Here we have to prove the identity     tan(x+π/3) = (√3+tan x)/(1- √3 tan x)

Q: 11. What is the exact value of tan (–105°)? O -2 + v3 O 2 - V3 )-2- V3 O 2+ V3

A: Given:        tan-105° Use the property:        tan-x=-tanx     Then,           tan-105°=-tan105°…

Q: Q4. Expand tan 0 in powers of [0 – ().

A: we have to expand tanθ in powers of θ-π4

Q: Prove the identity. 3 sin(x – y) cos y cos x 3 tan x - 3 tan y

A: Given that  3tanx-3tany=3sin(x-y)cosycosx We need to verify the given identity.

Q: nat is the period of y = -3 tan (2 n) +6?

A: Given query is to find the period of the function.

Q: 6. Do EITHER part (a) OR part (b) OR part (c). (a) Prove that, if n> 1 is a natural number, then…

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Q: Algebraically find all exact solutions to 7-tan(3-x)-4 /3 = 11 -tan(3-x) in the interval [0,2TT) X=

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Q: Verify the identity. 1+ sin(x) = (tan(x) + sec(x))² 1+ sin(x) 1 - sin(x) 1- sin(x) 1+ sin(x). 1 +…

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