29 yn C ini n0 Ca 22. Evaluate cos-1(sin ). 16 h cowor

Q: 3. cos? (z) sin“ (2) dz

A: Given, The integral is,

Q: 8. Evaluate T/2 (a) sin? a cos z dr | (In æ)? da. You may use In r dr = x lnx - x+c.

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Q: 1. Evaluate L(sin)) L(e-t cos 4t) 2. Is L(t? cos 4t) = L(t²)L(cos 4t)? c. %3D

A: 1c We have to evaluate Le−tcos4t. Apply Laplace transform rule: If Lft=Fs then Leatft=Fs−a. Here,…

Q: Find x where 0 <x < T. 2 cos?x = 1 Enter the smaller answer first.

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Q: Compute the indicated quantity using the following data. 12 sin a = 13 where = < a < T 2 cos B 3…

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Q: Find the Re(z) and Im(z) z=sin(e^i3)+sinh(5∠30)

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Q: S cos“ xdx = sinxcos² x + sinæ + c Select one: O True O False

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Q: Eliminate the parameter t in the following. x = cos 2t, y = sin t

A: Given that x = cos 2t; y = sin t To eliminate: the variable t Needed formulae: cos 2t = cos2t -…

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: Using an appropriate substitution, ſ sinº(x)cos³(x)dx is equal to: 10 coslx cos°x sin°x sinx + C 9.…

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Q: T/2 S cos () sin (æ) da = 2 COS (x) sın 0. O 15 2 O None 2 15 O 45 151

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Q: T/4 cos(8) 5r* sin(0) dr de

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Q: 3. * ... ... 35 21. Show work: trig ratio (sin, cos, or tan) of Z = = %3D trig ratio: =7' X =|

A: Given figure,

Q: Show that 0 π/2 st sin? xdx TT/2 [ 0 cos? rdr 2

A: A detailed solution is given below.

Q: Evaluate ycos z sin x dz. 3 3 7 + (*) cos (x) + cos? (2) 2 X syntax error. + C

A: Solce

Q: S sin³x /cosxdæ =? O a. ( ?cos'z – cosz) vcosa + C O b. ) +c rt), O d. (cosr + cosz ) /cosz + C C.

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Q: What is the exact value of cos ZPQR? 3. R. 21 16 7 16 3 16 4. 1/4

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Q: -T/2 Evaluate using Wallis' Formula: sins x cos6 x dx

A: Use Wallis formula.

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

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Q: 2. Which equatien will sllewes to sahve fer x? a sin 40= b sin 40 C. Cos 40 d. cos 40 e t 40= L t 40

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Q: S By an appropriate trigonometric substitution, S: I 1 √10 sin 0 cos² Ode Cos 0 10 sin 0 -do |…

A: Here we will use Trignometric sunstitution for given integral.

Q: Pu Pu n. %3D dy? is cos (r – y) -3r sin (x – y) e (x+ y)? sin (x – y)

A: In these type of questions there may be more than 1 options. Check all the options.

Q: ー49 a+ 22ト7 40 +3)Y-(sin 32) (Cos 2) +e

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Q: I don't understand how they got 10 square root of 6?

A: Given,

Q: 13:49 4 Screen. 34 (C) If y = sin 2x + cos 2x , then (y,)o =? ans. none PAE sin+ COs 2

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Q: CT cos 0+r sin 0+5 Evaluate: Si S (r cos 0) r dz dr de O 757/4 O 657/3 O 357/4 О 65л/4

A: Kindly note that there is a misprint in first integration limit .That should be 2 pi. So I have…

Q: 41 cos t dt = 1+ sin?t /2 If q sec e de, then a = b = and q =

A: Solve the integral in the following way:-

Q: dx 4. Evaluate cos? ' x (tan x + 1)

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Q: du u = ek sin-¹ m. m = sinx.k = 2² Iny,l == then at mv2 In 2 4 In 2 b) 2√2 rv2In 2 # In 2

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Q: H.w Evaluate;- Cos TT lt-1)idt

A: To evaluate:  1) ∫-∞∞δt-2e-tcosπt-1dt2) ∫03∫-∞∞t2+4δt-τdτ dt

Q: If /(sin(@))° cos(@)d0 = u' du, then u must be equal to Select one: O a. sin(@) O b. – cos(0) O c.…

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Q: 2) Find f' (=), f" (A), f" (E) given f (0) = sin 30 cos 0

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Q: Evaluate S eas cos?(y s) ds. V2

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Q: 17. x= sin t and y = 2 – cos´ /

A: Given: x=sin ty=2-cos2t

Q: Q 5. (a). Simplify the following by using Demoiver's theorem. (1 – cos 0 + i sin 0)6

A: Given  the given expression is 1-cosθ+isinθ6. Apply Demoiver's theorem cosθ±isinθn=cosnθ±isinnθ

Q: e. Find sin (x – y) given that sin x = 8/17 with 0 < x < 90° and cos y = -24/25 with 180° < y< 270°.…

A:

Q: 21) sin X 22) cos Z Z- A 30 40 Y 23) cos C 24) cos A 24 50

A: 21) sinX = 40/50 = 4/5 22) cosZ = 4/5

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

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Q: PPE Solu by hand 36(Cos 35+ J sin 30) 3((os 50°+ Jsin soo) Trignometric i

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Q: s).F ecosa sin a da cos a sin a da 2

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Q: 2π π14 cosφ SSS p' sinødp døde 0 0 0

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Q: Flag question T/2 S 3 cos (x) sin°(x) dx 15 15 None 6 15 45 2.

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Q: /2 89 cos t 9. dt = 1+ sin?t If q sec e de, then a = b = and g =

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Q: Using an appropriate substitution, f sinº (x)cos'(x)dx is equal to: cosl +C 11 cos 11 O Ths opton O…

A: We will find the integral by substitution as following-

Q: S sin? x dx Evaluate 1+cos x

A: ∫sin2x1+cosxdx

Q: T/2 S 4 cos? (x) sin° (x) dx = 3 O None 8 15 6 15 8 15 2 15

A: Topic- definite integration

Q: 13) sin z cos r dr

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

Q: 1 La So cos " dy dæ COS evaluate

A: We are given the Integral: ∫π2π∫0x21xcosyxdy dx=∫π2π1xsinyx×1x0x2 dx=∫π2π1x2sin xdx It cannot be…

Q: 15. (D? + 1)y cos x. y = c, cos x + c2 sin x + x sin x. ANS.

A:

Q: Compute the indicated quantity using the following data. 15 sin a = where <α<π. 2 3 cos B = - where…

A: We will proceed as follows...