Verify the identity. sin(x + y) – sin (x - y) = 2cos.xsiny

Q: i. An V21+3n an = 2¬" coS NT

A: We have to check whether given sequence is convergent or divergent. If convergent then find it's…

Q: sin³xdx ? 1- cosx Which Jof the following is one of the correct steps to evaluate A) None B sinydy +…

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Q: 2. Find the value of e a. 2 sin2 0 - sin 0 - 1 = 0

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Q: sin az sin z Given that J3/2(z) = V= - cos z compute cos az dz, where a az is a zero of J3/2(#).…

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Q: Determine the concavity and find the poir (a) y = 2 cos x + sin 2x, 0 < x < 2T %3D

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Q: |e2 sin²(e2«) cos(e24) dx. we let u =e2* To evaluate А) True B False

A: Given:       ∫e2xsin2(e2x)cos(e2x)dx      let u=e2x→du=2e2xdx           =∫sin2ucosu2du…

Q: 6. Setting æ = cos 0 show that T.(e) = [(- + ivI- =')" + (* - ivī- =')"] n where i = V=1.

A: This immediately follows as a consequence of De Moivres formula which states that e^(it)=cos t + i…

Q: 35. The cissoids r = a sin 0 tan 0. (See Exercise 29.) Ans. sin 0 cos 0 dr - r(1+ cos? 0) d0 = 0.

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Q: [et Suppose A(t) =0 0. cos t sin t, show that A(t)-1 exists and then find it. - sin t Co t. -

A: Given- At = et000cos tsin t0-sin tcos t To Show- Show that At-1 exists and then find it.

Q: Q2/ A) Prove the identity Sin (A + B) + Sin (A - B) = 2SinA cosB %3D

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Q: f Co3 n = and sin nLO, findi sin Can)

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Q: evaluate using the suggested method.

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Q: 1- cos A + sin A -then 2 sin A If y = is equal to 1+ cos A + sin A 1+ sin A

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Q: " f e/2i =sin2 then z = = sin2 then z =

A: In the given question we have o find the value of z which satisfies the condition s.t e-z2i=sin2.…

Q: W (1, sin x, cos x) =

A: Use formula for the wronskian is determinent form.

Q: TC + (c) Given that In = tan" x dx , show that %3D In + In-2 = (n 2 2) %3D Hence, find 8. tan (2x)…

A: Given an integral : In=∫0π/4tannx dx We need to show : In+In-2=1n-1 , n≥2 Also we need to find…

Q: Reduce to the form a + bi: a. sin (-i); b. cosh (1); С. cSc (1 + i); d. sinh (3 + 4i)

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Q: sin(z) = e-e 2i elz-e-iz ekte-iz 2i - 2i

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Q: What substitution should be used to compute | 1 dx? Q# -9 x = 3 sin (0) а. b. x = 3 tan (0 ) x = 3…

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Q: Find the z-values of cos i = e²

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Q: Sంబు ఒపా వింద ఇ + పిల్లయ 2-Sin LA Sin A tos A Sin A t cOS A 0.

A: Given : (2sin³A + 2cos³A)/(sinA + cosA) = 2 - sin2A

Q: 6. Setting æ = cos 0 show that T,(x) = [(r + VI– a²)" + (x – v1- x²)"]

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Q: m/s Let sin A = sin(A + B) cos(A + B): = tan(A + B) = with A in QII and sin B: X X X 8 - with B in…

A: Topic = Trigonometry As per guidelines, At a time only three sub-parts of a question can be…

Q: Determine the values of A, B and C. 2 x²V 4 - x2dx = A sin? t cos?t dt %3D

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Q: 1-sin e 5. r2 cos e dr de

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Q: 4 sin(A) – cos(A) | If tan(A) = , then %3D %3D 4 sin(A) + cos(A)

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Q: -cos x + sin x in the form r sin (x + a), where r> 0, is: e A. 2 sin x+ -sin |x+ 4 B 57 2 sin x+ 4 2…

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Q: 18.) Suppose x = R cos(0) sin($), y = R sin(0) sin($) and z = x² + y? + z? = R²Y R cos(). Verify the…

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Q: i1. L'[s/(s² +a)*]= (1/2a) t sin at 12, L' [1/(s² + a?)² = (1/2a) (sin at – at cos at) %3D

A: Introduction: The convolution is very significant in calculatig inverse Laplace transformation.…

Q: Z is a complex variable z=x+iy  question attached as photo

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A: Given: ∫-11x21-x2dx

Q: (1) Evaluate xdx Hint: Express cos* x in terms of sin x. Then use the substitution u = sin x. Back…

A: topic - indefinite integral

Q: 15. Evaluate Sin x cosx dx 2x Your answer 16. Evaluate se 3cos 2x Sin 2x dx Your answer

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Q: - Using Euler's equation, show that- : z fain (K 0)} - z sin Ø z2 – 2zCos Ø +1

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Q: (2{co(;)+ sin(;)})" Simpli fy, z = 1+v3i 0 22품 0 22플 O 42 O 24-

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Q: /2 sin'e cos'0 de

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

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Q: 2 sec? r 1 1 Prove the identity: 1-sin x + 1+sin x

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Q: .053 + 2.042 e(2.155+1.648/)t cos( sin( %3D

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Q: i. an V21+3n an = 2-" cos NT

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Q: 3. Evaluate L{4e¬2tt3 +t sin t cos t}

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Q: 0 ( -1 tan x du Q\ find dy if (xay sinx=(√√ au) - y² cosi'x

A: Given data:- x-ysinx=∫x2tan-1xdu1-u-y2cos-1x

Q: | b, sin nx cos mx dx — п

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Q: Specify it if the differetial equation is exact or non-exact. FInd the general solution. (cos2y -…

A: Given that: (cos2y-3x2y2)dx+(cos2y-2xsin2y-2x3y)dy=0