Q: If a cose - b sin 0 = c, Prove that a sin e + b cos e =+Va?+ b² – c² .

Q: Use the method of substitution to evaluate | 2x cos x² dx. sin x? + c – sin x? + c sin x? + c sin x-

A: We use substitution method

Q: a) cosx = - ja 0 <x< 360° b) sin (2x +) = 0, ja - << c) 2cos?x + sin +x) – 1 = 0, ja 0 <x<2=

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Q: Show that sin a – sin b < Ja – b), for all a and b. (Hint: MVT) use -

A: Mean Value Theorem :  The mean value theorem states that a function f which is continuous on the…

Q: Compute -i + cos -i sin a - sin a + i cos a where a E (T, ).

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Q: 3 with A e QIII , find sin2A 8 7. If cos A =--

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

Q: Suppose sin u=x and u is between 0 and 2. What is cos u? V1-x2 | VI- 2² 1

A: Consider the following equation: sinu=x Consider the following trigonometric identity:…

Q: If x = 4 sin 0, then J csc2ede = %3D

A: Here, ⇒x=4sinθ⇒sinθ=x4 By using Pythagoras theorem, We will have remaining side of the triangle…

Q: sin? Cos dx 2

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Q: Suppose sin u=x and u is between 0 and 2. What is cos u? V1- 22

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Q: So sin' z cos²z dr csc? z

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Q: If cos A with A in QIV , find sec %3D a. sec | b. sec 2. с. sec A d. sec 4-5 %3D A sec e. A2 1/2 II…

A: Since you are asking multiple questions. We are answering only the first question. Given, cosA=18…

Q: 8 Find the anti denivapine Sfa) faa or © f la) = Cos ( 6x) 16 - Sin? ( 6x)

A: f(x) = cos(6x)16-sin2(6x) ⇒I=∫f(x) = ∫cos(6x)16-sin2(6x)dx Since dsinxdx=cosx, therefore:…

Q: <O< 2T, sec(0)=9/4, find sin(0)=_ Suppose that places) (round to 3 decimal 2

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Q: If csc(z) = 6, for 90° <z< 180°, then %3D sin () %3D «(금) cos tan(플) - ||

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Q: A certain substitution gives S sin³ x cos" x dx = S(u7 – u5) du. What is n?

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Q: Determine c1 and c2 so that y(x) = c1 sin 2x + c2 cos 2x + 1will satisfy the conditions y(?/8)= 0…

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Q: If w=f(a,b,c)=cos(ab)sin(b)+c, what is at ( -,6

A: Given function and point is  w=f(a,b,c)=cos(ab)sin(b)+c and 12,π3,6

Q: If f cos xdx = A + B sin x + Csin²x+ Dsin³x+ E sin*x+ Fsin5x, what is the value of A + B + CD + E +…

A: Consider ∫cos5x dx =∫cos4x cos x dx =∫(cos2x)2 cos x dx=∫(1-sin2x)2cos x dx…

Q: If u(t) = (sin(7t), cos(7t), t) and v(t) = (t, cos(7t), sin(7t)), use Formula 5 of this theorem to…

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Q: O Find the anfidanialtiner Sfaw da for fla)= 18 Cos (6x) 16- Sin? (6x) © fa) = ¿* (, +x) 9 + xe

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Q: 1) Evaluate. x cosh ax dx

A: As per guideline we have to solve one question

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: What is the general solution of sin z sin ydx + cos rcosydy 0? %3D

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Q: 3. If v = sin- (4) + tan-' (±), find the value of r + y. 4. If z= ear+by. f(ax – by), prove that b…

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Q: a2z a2z dz Q3) A: If e-(sinx + cosy), show that ax2 ду? at

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Q: If  sin⁡x=e^y,  0<x<π, what is dydx in terms of  x?

A: Given sin x = ey   ..................(1) Differentiating both sides with respect to x  d(sinx) / dx…

Q: Q9: If F(x, y, 2) = [sinh-(sin- (In (/sin(cos(x²)) y? + zyx + y, find and ду az Q10: If z =…

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Q: Find all angles v between −π and π for which 2 √3 *sin(v)+2 cos(v)=2

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Q: Evaluate 3 cos z sin" e dz.

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Q: 1 tan z = 3'

A: The value of tanz =13  is given where, π≤z≤3π2 Solution: (a) Now  we have ,tanz =13, So -tanz will…

Q: Given that (-) x sin-1 -1 = COS eya. dy in the terms of x and y. dx Find

A: Given: xsin−1⁡1y=cos−1⁡eyx Since, dsin-1xdx=11-x2 and dcos-1xdx=-11-x2

Q: X sin²= cos7 zcos'dx ·COS 2

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Q: r = 12 sin 18ti + 12 cos 18tj

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Q: If 4 | sin*ea cos cx dæ 0, 35 then c=

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Q: Prove that, cos20 + sin?0 = 1

A: Let a, b and c be the lengths of right angled triangle. Then by definition,

Q: 22. Determine Sz sin? y cos y dy

A: Given that: ∫0π2sin2ycos6ydy

Q: Q12) If w=f(a,b,c)=cos(ab)sin(b)+c, what is at ( -,6 )?

A: Given ,fa,b,c=Cos abSin b+CPut 12,π3,6i.ea=12 ; b=π3 ; C=6

Q: Show that 7 sin? xdx L? cos? ædr I|

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Q: b) Explain how you would find sin" x cos" x dx if i) m is odd and positive, n is odd and positive,…

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Q: Using a suitable substitution, (sin x cos“ x) dx can be 4 (A) - f u*du (B)

A: Given: ∫0π2sinxcos4xdx

Q: one of sin x, cos x, and tan x is given. Find the othertwo if x lies in the specified interval.

A: Given that cosx=-513   and   x∈π2, π. This implies that, sinx=1-cos2x         ∵x lies in…

Q: y = C, sin at + C2 cos at, (a not to be eliminated)

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Q: Determine whether the following statement is true or false. If y = sin¹ (4x4), then = 16x³sin³ (4x4)…

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Q: derivation is required

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Q: find an eguation in X, y r Cos e 25 r Sin@= - 2

A: The objective is to find an equation in x, y.

Q: A certain substitution gives S sin*x)cos"(x)dx = S (u²-u*)du .what is n?

A: For substitution- Balancing the above equation, we can solve it as follows-

Q: If sin-r= In y, show that UTM dy (1-2) = y. dr

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