2. Use Euler's formula to prove the following expressions: (a) 1- cos(20) sin? ø 2 (b) sin(20) = 2 sin ø cos o (c) (W1 – w2),] [(W1 +w2). cos(wit) + cos(wyt) = 2 cos Cos

Q: 1. sin xsin ydx+cos x cos ydy = 0 2. dr = b(cos Odr+rsin Ode) 3. x cos² ydx + tan ydy = 0

A: According to our guidelines we can answer only one question and rest can be reposted.

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: Verify the identity. 4 cos(sin-1 x) = V 16 – 16x? Let e = sin-1 x = sin e = x = X. * Thus, 4…

A: Explanation of the answer is as follows

Q: 5. (a) Expand (1+x) and hence find the value of (1.02) correct to 4 decimal place 1+sin 0 m-1 1-sin…

A: First expand 1+x4 then find the value of 1.044 Using the identity, a+b4=a4+4a3b+6a2b2+4ab3+b4…

Q: -1x 54cos If cos -1 00, prove that b. a x² 2xy ,2 = sin C. COS a+ ab %3D 2

A: Introduction :

Q: 10. y = C, cos 4x + C2 sin 4x + C3xcos 4x + C4xsin x + C5; C, to C5 are arbitrary constants

A: Since their are 5 arbitrary constants so the differential Equations will be of order 5. We find the…

Q: 5. In AABC, m2B = 90°. sin A = 2x + 1.5 and cos C = 3x – 0.9. Find x.

A: Given: In Triangle ABC∠B=90οsinA=2x+1.5cosC=3x−0.9x=?

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> 0

Q: A-Show that S 1, L{cos at} s2+a²

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

Q: [o,1] Find the sne exponsion of fla)=x+2 in in Sine Sinlntix), %3D 00 4-(-1)^ %3D •Sin (nTx) (c) Sin…

A:

Q: 2. : (a) For n ≥ 1, show that 1+z+2²+...+ 2¹: (b) Hence, show that 1+ cos 0 + cos 20 + 12+1 2 #1 7…

A: Solution:

Q: If z = +i then Im(coshz) A) –sin1sinh4 B) cos1cosh4 e* +e* C) cos1 2 D) sin1cosh4 E) sin1

A: Topic:- hyperbolic function and complex number

Q: 1. Find the exact solutions to following in the interval [0,27) a) v2 cosx -1=0 b) tan e = -1

A:

Q: Let z = 8(cos 50° + i sin 50°) and w=2(cos 30° + i sin 30°). Express in the form r(cos+ i sin 0):…

A: Here we can use the following formula to find the results eiθ=cos θ+i sinθande-iθ=cos θ-i sinθ

Q: 15 and x terminates in guadrant III. 17 Find sin2x, cos 2x, and tan 2x if sin x= - sin 2x cos 2x %3D…

A: The solution is given in the next step.

Q: In the process of calculating that: cos³ (112) de a substitution is made in the variable u, then it…

A: Given query is to find the integral after substitution.

Q: 8. 3. (1 – cos wt) where w is a positive constant

A: In given options, 4 is taken instead of "w^2".  The solution for the asked question with correct…

Q: Given that sĩn = %3D 2 |cos 플 호 and COS %3D sin = cos 4 = show without Ee using a calculator that…

A:

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: the solving for equa tion ty=o is 1-y= COSX %3D 2-y= Sin x %3D y= tax

A:

Q: Q2/provethate Cos17 +SinI7 cos17-Sın17 %3Dtun62

A: We have to prove that                               cos17°+sin17°cos17°-sin17°=tan62°

Q: er +6 近 。 Oe) sin(2a) Od) cos(2x) T SOƆ 7 5 Ob cos(x²) + 2x (,r)so) (e O ap UIS .2 hip If y =…

A: Topic :- Derivative Correct option = C

Q: 32. If 2 sin 0 cos 0 cos 0 =0, where 0 <0 < 2n, then the exact values of 0 are 57 0, 3 O0, 5. 7, ,…

A: Given : 2sinθcosθ - cosθ = 0 Where, 0 ≤ θ ≤ 2π To find : Exact value of θ?

Q: Answer: The approximate value of sin 29° is O sin 29° s 1( 29x 2 180 6)+ O sin 29° V3 ( 29x O sin…

A: Please see the explanation below

Q: 3) Solve For OsO<2M VZ COS O + 2öin20=sin 20

A:

Q: Q1: (1) Show that the value of € (-1, π), for which: sin² 0 1+ sin² 0 sin²0 1 + cos²0 cos² 0 cos²0 4…

A:

Q: 0° S (c) Prove that: 2cos 20. cose 2 + 2 tan0. sin0 = %3D cos?e – sin? e cose o AEGW is drawn.

A:

Q: 2.Expand the following in powers of x i)√(1 + sinx) ii)e cosx iii) cos x²+

A: Given data:- (i); 1+sinx (ii); excosx (iii); cos-1x2-1x2+1

Q: If f(1, y) = e“ sin 7y, then fay is given by: o - 28 et sin 7y O - 28 e“ cos 7y O 28 e" sin 7y O 28…

A: Given that: f(x,y)=e4x.sin7y

Q: Solve the following over the interval [0, 27]; Sin 2x Cos *- Sin x = 0 O 0, 0, 6 O 0, 7, 2m, , O 0,…

A: Given sin2xcosx-sinx=0 The trigonometric identity used is sin2x=2sinxcosx So the expression becomes…

Q: Consider (e cos 4 + ie sin 4) (11+12:) cos 4+ ie sin 4) (11+12i) 3DZ What is the general value of z?…

A: Euler's formula is given as that e^(ix) = cos(x) + i sin(x).

Q: 2. If 90° < 0 < 180° and cos 0 =-, find sin. %3D 11/3 11/3 3 ) - 3V11 11 O 3/11 11

A: We know that the trigonometric identities :  cos x = 1 - 2 sin2 (x/2)

Q: 1 with in Ql , find sin B = B If cos B B Cos 3- 2/2 6 3- 2/2 Cos B COS 22 3 B cos 3 + V3 3 + 3 Cos 6…

A:

Q: /Prove that the value of cos()dz, when z = T + 2i is e + e-1

A: Complex integration of the function

Q: 1-Find the Cauchy principle value (showing details): J_co (7*+5x²+4)' cos(4x) dx 8.

A:

Q: 1. Express as a sum or difference a.) sin 7t sin t b.) cos 6u cos (-4u) c.) cos 2t sin 6t d.) 2…

A:

Q: 2 (cos Fe tisin) - fsih 똥) Q) put Vz (cos 3+P sin I) 6. in expoitial hor m

A:

Q: a Show that (sin(m + n)x + sin(m – n)x) b Hence, without using the product rule, differentiate sin…

A: We will find out the required values.

Q: 7.32. Prove that for 05sr, -( . ) cos 2 cos (a) a(e -a) = sin 3r sin ba (6) (r-) - 7.33. Use Problem…

A:

Q: Given that cos(2t) = 2 cos (t) – 1, it follows that L{cos"(t)} =;( +:). O True O False

A: We need to find Laplace Transform of f(t) = cos2(t) But , cos2t = 2cos2(t) - 1  ⇒ 2cos2(t) = 1 +…

Q: Solve the following equation on th e interval [0, 27]. cos x + 2 cos x+ 1 = 0

A: Given : cos2x+2cosx+1 = 0

Q: 8. Find all values of 0, if 0 is in the interval [0°, 360°) and cos 0 V3 2

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: Solve for O on Co, 2T) 6 sinio + 9 cos 0 -9-0 2 Sin O + 3cos o -3=0 Sin O +los? = Sm?O =1- cos?O…

A: Form the given trigonometric equation in the quadratic equation than solve by factorisation.

Q: Find sin 2x, cos 2x, and tan 2x if sinx= and x terminates in guadrant III. V13

A:

Q: Solve the equa tion on the interval [ o, 2 ) 2 sin? 9-3 sin O +1 =0 tan2x-1 =0 (2 cos x +JE) (2 sin…

A: As per bartleby guidelines we only give first three question answers.

Q: For how many a E (0, 1) will sin(x) + a sec(x) = cos(x) + a csc(x) have at least two distinct…

A:

Q: b. cos(3n) + 2 sin(3n)

A: Solution :-

Q: Find the values of z satisfying cos Az = 0 2

A: Result : General Solution of  cosx=0 is x=(2n+1)π2

Q: 22-j is 1. -1+jZ If Z = cos 0 + j(1+ sin 0), show that the magnitude of

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.