cosh (T– i) = eT cosl - i eT sin 1 + e-" cos 1 + ie- sin 1 - IT 2 e cosl - i eT sin 1 + e" cos 1 + ie- sin 1 et cosl + i e sin 1 - e- cos 1 + i e sin 1 2 e cosl - i e™ sin 1 + e- cos 1 i e- sin 1

Q: cos(a

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Q: esin'x csc 2x(en * – 3) sin?

A: let u=esin2x-3⇒dudx=ddx(esin2x-3)          (ddxex=ex,ddxa=0)    dudx=esin2xddx(sin2x)-0…

Q: Show that u(x, t) = 4 tan-1 I-ut ev where v is constant, is solution of Uxz – Utt = sin(u)

A: To check the given solution satisfy the given partial differential equation, substitute the solution…

Q: cos' x+cos'x dx is sin x+sin'x Q 9. The value of the integral

A: Introduction :

Q: sin 0 cos Od0 -u'du FC = - 1 cos“ 0 + C 19.

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Q: 2- S x. Sin (5X) dx : Cos (SX) Cos (SX) Cos (SX) XSin (SX) XSin (SX) 25 25 25 P+9 P+9 P-9 3- L{e.…

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Q: Q4) Find y" + 2y' + 5y where y cos(1/secx)

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Q: . Differentiate each function. a) y= cos'x b) y= sin(x³)

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Q: sin(20) 0 = /-

A: When theta is between 0 to 360 degrees, then 2theta is between 0 to 720 degrees. We use sin inverse,…

Q: S 1 dx = (x² + 1)(1 – sec(tan-1 x)) Select one: а. 1 -x + (sin(cos-1x)) b. 1 -tan(cot-1x) +…

A: Hence option (d) is correct .

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

A: Part (d),Given,Sin(sin-10.8)

Q: 2 + sin x Differentiate Y x + cos

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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: 3+2cosx dx is equal to (2+3cosx) sin x 2 cosx 2+3cos x) 2+3sin x 2 cos x 2 sin x (d) 2+3cosx 2+3sin…

A:

Q: tan 2x sec 2x dx Evaluate cos 2x O 1 ,tan 2x e + C 2 2 e tan 2x + C O -2 e sec 2x + C 1 ,tan 2x + C…

A: ∫etan2x sec2xcos2x dx=∫etan2x sec2x sec2x dx     ∵secx=1cosx=∫etan2x sec22x dx Now put,…

Q: sec^2 y - tan^2 y = sin^2 y + cos^2 y

A: Consider the trigonometric identities mentioned below.

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: Find y': COS X y = 1-sin x O y' = sin² -sin x-cos² x (1-sin x)²

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Q: sinh (u+v)=sinhycoshr+ coshuxsinhv

A: Use hyperbolic function

Q: Š 4 sin(3t) 2+ cos(3t) 7 sin(3t) + dt (2+ cos(3t))²

A: Definite integration

Q: Differentiate. ' a) y = 2cos(x²)

A: Hi, at a time we can answer only one question and the exact one was not specified. So, I have…

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: 1 + sin x Differentiate y = x + cos x

A: As we know that: The Quotient rule: fg'=f'·g+g'·fg2 The Power rule: ddxxn=nxn-1 Given:…

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: Evaluate x2 dx Select one: on O(sin (2r- 1) + 2(2 (2ain (r) + sin(2si To (stn(2 1I) 2(2r sin(2sin

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Q: Compute y' for y=√(3x++ e - 3x) 8 A (В B D Say 3 24 y = ²4 (4x³ - e-³x) (3x + + e-³x) ³ 5 3 8…

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Q: decimal place by using a small enough interval. g'(8)≈ Let g(t) = (0.4)'. Estimate g/(8) to within…

A: Choose the small increment say ∆x =0.1 Then we know the definition of derivative gives ,   f'(c) =…

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

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Q: cos2x- sin2 cos2x For dr=F(x) +C What is F(x)? cOSx-sinx A -3 sinx- cosX 2. Cos - COSX+sinPx 3 B…

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Q: Ir x²y" + xy' + (x? - +>v =0 x >0 || | 1 - 2 sinx ,V1=X the following equations satisfied by v and y…

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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: