(a) Prove that, if n> 1 is a natural number. then tan"-(r) /- tan" (r) dr. 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: Prove the following identities and give the valuesof x for which they are true

A: Let tan-1 (x)=α⇒x= tan αHence, we have tan 2α=2 tan α1-tan2 α

Q: Find the exact value of 2tan 15° /(1 - tan2 15°)..

A:

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: Prove that: (1 – sin? x)(1 + tan? x) = 1

A:

Q: 5. What is the exact value of tan 195°? O 2 - V3 2 –

A: Using advanced trigonometric identities we can solve for tan 195o

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

A: Introduction :

Q: Question # 1 Apply De Moivre's Theorem to prove that 5 tan 0 – 10 tan'0 +tan³ 0 1- 10tan²0 + 5tan*0…

A:

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: (a) i) Prove that 1 sin20 1 tane 1+ sin20 1+ tane for 0<0 <- 4 ii) Hence, show that the exact value…

A:

Q: B) Prove that: 1-tan? 0 cos? 0 – sin? 0 1+tan? 0

A:

Q: Develop a formula for cos(3θ) as a third-degree polynomial in the variable cos θ.

A:

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

A: The solution is given below :

Q: Prove the identity 1+ tanz 1- tanz - t (-+ ) tan (

A:

Q: Using poner seYies for tan x prove that ī = 2 53 Ź (2n+1)3"

A: According to the given information, it is required to use power series of tan inverse x to show…

Q: 3b) Compute tan 6. An exact answer is required.

A:

Q: 1 Use the inequality sin xs x, which holds for x20, to find an upper bound for the value of sin x…

A:

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

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

Q: 8. [Essay] Find the approximate values of tan44.5

A:

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

A:

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

A: Topic = Trigonometry

Q: what is the general solution for -1=2tan(x) + tan2(x)

A: Simple calculation of trigonometric ratio

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

A:

Q: The solution of tan x = -V3 in [0, 7) is x = 7 If n is any integer, all solutions of 3 or x = tan x…

A:

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

A:

Q: 2 sin 50 do. 9. Use the residues' theorem to evaluate sin o

A:

Q: 4. Use an identity to find the value of tan (6– 180°). O - tan 0 tan 0 1 O-1

A: 4. We need to evaluate the value of the following quantity tanθ-180° Identity Used : tanA-B =…

Q: Let x= 2 tan theta, 0 less than or equal to theta < pi/2  simplify the expression  1/x^2…

A:

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

A:

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

A:

Q: 1-tan20 = 1- 2sin?0 1+tan20

A: 1-tan2θ1+tan2θ=1-2sin2θ Formulas 1+tan2θ=sec2θ1-cos2θ=sin2θ 1secθ=cosθ

Q: Find all values of x in the interval [0,360) that satisfy the equation. Use degree measure.…

A: Given

Q: (a) Prove that the equation has at least one real root.(b) Use your calculator to find an interval…

A:

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

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

Q: Prove that there is a real number r so that sin(r) = x – 1.

A: We have, sinx=x-1 Let us consider a function fx such that, fx=x-1-sinx

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

A:

Q: Prove one of the following identities. 1-tan2 x 2 tan x Cos 2x = sin 2x 1+tan2 x 1+tan² x

A: Please check step 2 for the solution.

Q: Find the exact value of the expression. tan(8t/7) – tan(1/7) - 1 + tan(87/7) tan(n/7)

A: The expression is: tan8π7-tanπ71+tan8π7tanπ7 To find the exact value.

Q: 5.6 Locate the first nontrivial root of sin(x) =x² where x is in radians. Use a graphical technique…

A: Given that sin(x)=x2 Let f(x)=sin(x)-x2 Graph of given function is In the figure,  we see that…

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

A:

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

A:

Q: Using the fact that sin θ and tan θ are both periodic functions, calculate sin (325π/ 4) and tan…

A: Using the fact that sin θ and tan θ are both periodic functions, calculate sin (325π/ 4) and tan…

Q: 9.2. If z1, z2 # (1/2) + kT, show that tan 21 = tan z2 if and only if 21 = 22 + kT, where k is an…

A:

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.