Quèstion 10 cosh (T- i) = e" cosl - i e" sin 1 + e- cos 1 + ie- sin 1 e cosl - i e sin 1 + eT cos 1 + i e" sin 1 - TT eT cosl + i eT sin 1 - e-" cos 1 + i e- sin 1 - It 2 e cosl - i e™ sin 1 + e- cos 1 - i e-T sin 1 - TT - It

Q: *T/3 sin0 + sin0 tan²0 do sec²0 6.

A:

Q: Question 6 Find the solution. (4D3+12D2+13D+10)y = 0. /½(c,cosx+c_sinx) + cge -2x y = c ,xe-2* + e A…

A: given differential equation is  9D3+12D2+13D+10y=0            (i) Solution of the Homogeneous…

Q: Question 5 Evaluate the Integral / costx sinx dx (A 5 -cos x+C (B) -sin³x+C -sin*x+C -cosx+C D

A:

Q: QUESTION 2 For cos2(xy) =- evaluate y when x = 1. 4 3 6. 3

A:

Q: -1 (d) sin(sin¬! 0.8) (e) tan-'(tan ) (f) sin¬'(sin 2)

A: Part (d),Given,Sin(sin-10.8)

Q: Eliminate 0 from the equations : (i) x = h + a cos 0, y = k + b sin 0 (ii) x = a ser³ 0, y = b cot³…

A: Solution is given: Hope the solution is helpful.

Q: 5π (b) sec 6 (c) (sin 570⁰ + cos180°)-¹ (d) sec 7π 6 - 1 CSC 4π 3 + COS 5π 6

A: b)sec-5π6-csc4π3sec(-θ)=secθ since you have posted multipart question, i can do first question as…

Q: Take the Laplace transform of the following initial value and solve for Y(s) = L{y(t)}: sin(π ) ,…

A:

Q: 3. V2 C T. V2 V2 3 10. sin B =[Select ] 11. cos B = [ Select ] 12. tan B = Select] - -13

A: Trigonometric ratios

Q: Find y': y = ar cos

A: The given function,  y=ar cosx3

Q: Evaluate: e* cos (7e*) cos (4e*) dx - sin (3e*) + –sin (11e*)+C A 22 B - sin (3e*) – –sin (11e*) +C…

A: Evaluation of the Integral

Q: Question 9 Find tan'r sec?t dt A - tan²t+C B tun't + C tan" Isec*t +C_ an*r+C 4 D

A:

Q: Find y' where y where y = 10 sin-1 (cos (21 z)) - tan C BARANG (18 r)

A: Given: Now,             y'=10arcsincos21x-arctan18x'     =10arcsincos21x' -arctan18x'…

Q: 5. 4 (secx-1)(sec² x+secx+1) Sª cos² 2x-2 cos 2x+1 -dx

A: Indefinite integral is the process through which one can determine the function which on…

Q: V3 Tan" (-V3) Cos"(-1) 3. Sin 2 1. 2.

A:

Q: r = 2 cos(4 e) r= 1+1 sin(0) r = 3 cos(2 0) r = 1+ 4 sin(e) r = 3 sin(3 0) r = 3 - 2sin(0) %3!

A: To match the given figures with the given equations.

Q: Find the equation for a sine function with: 32 • Amplitude = 3 • Period = • Phase shift = (-) n •…

A:

Q: Evaluate OI 4 sin ³x dx sin*x + C -sin¹x + C +cos³x + C -cost + +C cost --cos³x + C

A:

Q: how to find cos z using, cos^2x +cos^2 y+ cos^2 z=1     where x = 45deg  and y = 60deg

A:

Q: 0 a "/2 ((+ cos@)-1)sin@d0 + a |((1+ cose) - 1)sinede 3 3 a ("/2 (1+3cos@+3cos 0+ cos 0-1)sin@de a3…

A:

Q: Differentiate y with respect to a y cos²(a) + y sin²(a) = (cos(a)+37)² Select one: O a. y' =…

A: ycos2a+ysin2a=cosa+372

Q: Question 7 Find dy/dx. y = x$ sec (–) (A x3 sin 5x cos x + x² sin² 5x () B -x3 sec + 5x4 tan sec (c)…

A: here problem of differentiation we use d(u*v)/dx rule d(u*v)/dx = u*dv/dx + v*du/dx so answer is…

Q: Sin2 1T sin? 5

A: Given: prove that sin27π8+sin25π8+sin23π8+sin2π8=2 we know that sinπ-x=sinx…

Q: : Se' com (7e')cos (4e")de Evaluate: (A) -cos (3e") –cos (11e*) +C 22 -cos (3e*) + -cos (11e*) +C B…

A:

Q: Select the general solution to the equation. y" + 16y = 0 %3D Oy= C1 cos(-4x) + c2 sin(-4x) Oy= cie…

A:

Q: tollowing. 1. sin(sin)

A:

Q: S(csc x cot x + 8x")dx - sin x + x8 + c - sec x + x° + c CSc x + x° +c CSc x + x° +c - sec x + x° +c

A:

Q: .cost x - sin* x = cos 2x : a Wáillánp Eu /3ew

A:

Q: (a) (1+x)1+6x

A: (Solving the first question as per our guidelines) Solution of (a): We have to show that 1+x6≅1+6x

Q: V5 sec² 0 V5 sec 0 Why is = sec 0? Because sec2 0 = (sec 0) (sec 0) Because sec2 0 = tan² 0 1…

A: From the given problem: 5sec2θ5sec2θ=secθ

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.