2 10) Given sin A = - where

Q: 20 a Show that sin (A + B) + sin (A – B) = 2 sin A cos B. b Hence find: i 2 sin 3x cos 2x dx ii sin…

A:

Q: Eliminate the parameter t from the following. x = sin t − 5, y = cos t − 4

A: Eliminate the parameter and simplify it.

Q: π/4 1 π/4 sin TX cos 2y sin 4z dy dx dz = 0 0 0 (Type an exact answer, using n as needed.)

A: Solution

Q: 8. 4 sin(at +b), where a and b are constants.

A:

Q: (1–tan? x) = cos x on the domain 0 < x < 2T. Solve (1+tan? z) 27 O T, 3 п, 품, 뚱, 47 3 27 O , , 2ㅠ 57…

A:

Q: 2 Given tan 0 = -and sin 0 > 0, find cos 0. %3D Cos 0 _ 3/13 13 О А. O B. cos O 0 = 3/13 COS %3D 13…

A: The given data is: tan θ= -23  and  sin θ&gt; 0

Q: 1. Determine solutions to sin 2x = , x€ [0, 2x) 2x sin() 2x 0.73 %3D %3D accurate to 2 decimal…

A: Explained below

Q: 1. Determine solutions to sin 2x = , xE [0,2x] 2x sin () accurate to 2 decimal places. 2x 0.73 X0.36…

A:

Q: 3. у %3D In(5 — е**) 4. x = et (cos 2t + 2 sin 2t)

A: Now the first given function is ln5-e4x The second given function is x=etcos2t+2sin2t To find the…

Q: 10. Suggest ways to avoid loss of significance in these calculations. (1) Vx² +1-x; (3) sin x- tan…

A: 1 x2+1-x By rationalization  =x2+1-xx2+1+xx2+1+x=x2+1-x2x2+1+x=1x2+1+x Therefore, as x→+∞ there…

Q: 3 T 3. Find the exact value of sin 8. 1 + cos 0 - cos e 1 = + cos = ± sin cos O tan 1 + cos 0

A:

Q: 15. Given that sin(1.4) = 0.99, determine the value of sin(2T +1.4). 2n 0.99 O 0.99 27 + 0.99 O…

A: Given : sin(1.4) = 0.99  sin(2π+1.4) = ?

Q: If 0 < 0< and z= (sin 0+i(1- cos 0)) find in its simplest form arg z.

A:

Q: 06:- Find the result of the following. (Choose two only) 4 1- 2-Si(Vx+ dt OLLI x² 3- 7 sine do

A:

Q: 2. If tan 0= x2, which of the following is correct? Defend your answer. a. cos 0 = 1/V(1+x^4) b. sin…

A: The solution for the above question is as shown below

Q: 12 5 - and csc y = - 13 where a < x < and < y < 2n, Given cos x = find the following: 1. sin(x + y)…

A:

Q: 1. f/² sin () cos (+) sin (²) d dx (Consider initially the first 2 terms)

A: We have to use the formulas for 2sin(A)cos(B)-sin(A+B)+sin(A-B) and 2sin(A)sin(B)=cos(A-B)-cos(A+B).…

Q: f(A) is an odd function, and deduce that for each x E R the value of the c) Show that integral 3A…

A: From part (a), the function f⏞λ is defined by f⏞λ=i2π3λcos3λ-1λ2sin3λ Relacing λ by -λ,…

Q: 18 a Show that / (1 + sin 2zx)dx = n, for all positive integers n. b Sketch y = 1 + sin 27x, and…

A:

Q: 1.)When m is odd, we can integrate sin" (x) dæ by letting u cos(a). Why does have to be odd for this…

A:

Q: In the interval 0 <z< 2n, for what value of x does sin a = cos x? and 4 4 only 4 and 4. 4. - only…

A: sin x=cos x implies tan x=1

Q: 4. (a) Express 3cos x-4 sin x in the form R cos(x+ a) where R>0 and 0 <a < (b) Hence find the…

A:

Q: 1. Consider the equation cos x tan x 1. sin x a) Show that it is true for x = 30°. b) Show that it…

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

Q: 1. Determine the value of cos(2x+2y) if sin z 3 and tan y = - for 4 sysa. for 0sxs: VI VI

A: Given : sin x = 3/5 and tan y = -3/4

Q: Particular Solution of the equation (sin x) y' = y satisfying the initial condition y(7/2)=e is, (а)…

A:

Q: When t = 0, AP = ..... so sin t will begin at a value of 0. As t increases from 0 to 7T/2, sin…

A:

Q: How many values of 0 in the interval 0 < 0 < 2T satisfy 1 – 3 sin 0 + 5 cos 30 = 0? %3D (A) 2 (B) 4…

A: The aim is to determine the number of values of θ in the interval 0≤θ≤2π satisfies 1-3sinθ+5cos3θ=0.…

Q: 4. sin M= 20 16 30 5. tan L = 6. cos Z = 16

A:

Q: Eliminate the parameter t from the following. x = sin t − 3, y = cos t − 2

A: Eliminate t by squarring

Q: 1) Using the formula: cos(x + y) = cos x cos y - sin x sin y, prove in steps that: cos? x = 1+cos 2…

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

Q: 2/12 6. If sin(t) =- and cos(t) < 0, find the exact value of tan(t). %3D

A:

Q: 2. Find all the exact solutions to following. a) sin x= 0 b) tan e = 3

A: If sin x =0 then x=nπ ; where, 'n' is any integer .If tan x =3 then x =nπ+π3 .

Q: 1. For non-negative integers n, let k +1 k +2 Σsin n +2 n sin k = 0 n +2 f(n) = Lsin-( k +1, k = 0 n…

A: Given f(n)=∑k=0nsink+1n+2πsink+2n+2π∑k=0nsin2k+1n+2π

Q: 6. Evaluate |2 Sin xʻdx, by (i) mid-point rule, and (ii) Simpson's 1/3 rule.

A:

Q: Suppose that sin(a) = 4/5 and cos(b) =4/7 define in the first quadrant, determine tan(a+b). (round…

A: Given, sin(a) = 4/5 ------equation 1 cos(b) =4/7 ------equation 2

Q: How do you solve this?

A: Given that cos x = 1/3 and x is in the interval (0, π/2).sin y = 1/2 and y is in the interval (π/2,…

Q: 4 sin 2t + 2 tan 2t = 0 %3D

A: 4sin2t+2tan2t=0

Q: 1. Find the exact value (not a decimal approximation) for sin(22.5°) (Hint: 22.5 = 45/2)

A:

Q: 5. Given 0 < 0 < 27, solve cos² 0 = 1 – sin 0. ○0, 플,T O 0, 플, , 플

A:

Q: 9. Prove that | sin n0/sin 0| <n, limiting values being used when sin e = 0.

A:

Q: 1 3. a) Verify that sin x cos x = tan x--- π for the value x =-. 4 Ls Sin 4cos 4 2.s TanT/4-Y2 しS…

A: We can use the concept of trignometrical ratio in order to solve the given problem.

Q: 1. Given 0<0 < 27, solve tan 0 = 0. %3D )号,警 O 0, 7 O O

A: In this question we have to find the value of x at which tan x =0

Q: 1) Using the formula: cos(x + y) = cos x cos y – sin x sin y, prove in steps that: cos? x = %3D…

A: Note - Since you have posted multiple questions, I am answering first one for you as per the…

Q: 3. (a) Use the substitution x = 2 tan 0(-1/2 <0 < T/2) in the expression T/V4+x2 and show the result…

A:

Q: 5. Given 0 < 0 < 27, solve tan 0 = 0. 2 2 O 0,

A: Given:           0≤θ≤2π , tan(θ)=0

Q: 40 0<0<-, find the exact valı 41' If sin 0 = (a) sin (20) (b) cos (20) (c) sin 2 -

A:

Q: Compute the indicated sin α = 15 17 cos B = cos = (a) (b) - 4 5 quantity using the following data.…

A:

Q: -1 Find y' where y = 22 sin-(cos (9 æ)) – tan (6 æ) Answer: -198 sin(9 x) 1 || V1-cos2 (9 æ) 1+36 x2…

A: To find y'

Q: 3) Find the exact value of cos(a + B) under the given conditions. V5 0< a < sin ß = - -< B < 0 4 TC…

A: We know thatcosα+β=cosα cosβ-sinα sinβ

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.