$5. (i) show that: sin 0+sin 20 = tan 0 1+cos 0+cos 20 (ii)Find the general solution of the equation sin 4x + cos 2x = 0 (inSolve for x ,where0 sx aj the equation sin 3x + cos x = 0

Q: 32. y" + y = sec x; y = c1 cos x + c2 sin x + x sin x + (cos x) In(cos x), (-7/2, T/2)

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Q: Evaluate the definite integral.

A: Given : The definite integral is ∫π 3π 2  cos x ( sin x )sin2 x -14 dx .

Q: 3 S² x³ cos x ²dx 6.

A:

Q: (1–tan? x) = cos x on the domain 0 < x < 2T. Solve (1+tan? z) 27 O T, 3 п, 품, 뚱, 47 3 27 O , , 2ㅠ 57…

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Q: 6. y" + 3y'-2y e-2* [(4+20.x) cos 3x+ (26-32x) sin 3x]

A:

Q: 2. Solve for y in terms of X for the following equations: a) In(1- 2y) = x b) In(y- 1)- In 2 = x +…

A:

Q: Sx' cos(x4) dx = o 1 cos(x*) + c 4 - -1 - cos(x*)+ c 4 1 sin(x*) + c 4 -1 sin(x*) + c 4

A: *concept :- let, x^4 = t then integrate the simplified term cos(t).

Q: a 1 - x²) cos(nx) dx F(x 一九 4 sin(nл) — 4nл соs(nл) — 2n²л² sin(n) πη3

A:

Q: + 5x + 6 cos x + 2)dx = e – x + cos a + 2 + c - O 3e* + x³ + 6 cos x + 2x + c 3et + x + 6 sin x + 2x…

A: We need to evaluate the following integral I = ∫3ex+5x4+6cosx+2dx

Q: cos 2x he ƒ -dx is 4+sin 2x {A} In|4 + sin 2x| + C {B} In|4 + sin 2x| + C {C}(4+sin 2x)² + C {D} -(4…

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Q: 2 3) Find the general solution to y' = sec x. 4) Find the particular solution to y' = sec x tan x…

A:

Q: 2. i) Find in radians the values of x in the interval 0°0 and 2 is and acute angle. Hence find the…

A: The problems with the trigonometric functions for value of x can be solved using the trigonometric…

Q: 14. x" + y = -101 sin(10t) ; y " + x = 101 sin(10t) ; x(0) = 0, x ' (0) = 6, y(0) = 8, y' (0) = -6

A:

Q: 1) Solve for r; 0 <x < 2ñ. sin n r – sin r = 0

A: To find the value of x ,first we take common factor sin(x) outside.Then we get two equations…

Q: 2. (sin 0-2r cos 0)dr + r cos 0(2r sin 0 + 1)d0 = 0

A:

Q: coS x dx 6) 1 + 3 sin x A) In| 1+3 sin x|+C C - 를 In| 1 +3 sin x| +C

A: To evaluate ∫cosx1+3sinxdx

Q: /2 2 cos x dx 1+ (sin x)² -n/2

A:

Q: 13. sin? 4x cos² 2x dx T/2 14. S sin? x cos³ x dx

A:

Q: 4 sin(x) cos(z) + 2 sin(z) – 2cos(z) – 1 = 0

A:

Q: a) _*? (1-x²)Z x+3 b) S- x2+2x+5 c) Find the value of sin(tan-1- sec-d) dx d) S x² Vx2+1 e) S Vx2+2x…

A:

Q: 1) x² sin(y') + xe2 – cos(z?) = 3y– 6z + 8 cos(z?) = 3y – 6z + 8 %3D -

A: Given; x2siny3+xe3z-cosz2=3y-6z+8 Now differentiate partially with respect to x we get,…

Q: Sin x 10. y = 2+Cos x 3 2+Cos x Ob. (2+Cos x)? Cos x C. (1+Cos x)2 1+2 Cos x d. (2+Cos x)? Oa.…

A:

Q: 5. (sin 0 – 2r cos² 0) dr + r cos 0 (2r sin 0 + 1) d0 = 0

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Q: 4 sin"t- cos *t= sint- cos 4 2 2

A:

Q: 2 Find the x-intercepts of y = 2 sin x + sin x – 1 on the interval [0, 27). %3D

A:

Q: (-1)° x*1 (2k –1)! 2k-1 k=0 a) sin x b) cosx c) sin x- x d) cosx-1 e) e* ||

A: Given,

Q: S cos ( x^3 ) dx = * sin ( x^3) + c 3x^2 sin (x^3 ) + c - sin (x^3 ) + c - 3x^2 sin ( x^3) + c none…

A:

Q: iFind the general solution of the equation sin4x 19. Find the general solution of the equation cos2x…

A:

Q: 1. S 2x sin-1 x² dx. 2. S sin² 20 cos³ 20 d0. 3. S sec? x dx V1-tan?x

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Q7: Í sin(3z)cos(4z) dz = a)cos z- cos(72) + C b) -tcus x -os(Ix) + C %3D Qe S sin'x cas d = 2).

A:

Q: 3 8) 1--sin (2t) = sin' (t) + cos (t) sin(t) + cos(t)

A: Given,            1-12sin2t=sin3t+cos3tsint+cost

Q: 2. (a) Show that V3 cos x-sin x COS where 0<x<2r . 2 (b) Using the result in (a), solve the equation…

A:

Q: 12. Which is not a solution to the equation sin x = cos x-1? %3D A. x = 1 B. x == C. x = 3n 13.…

A: We will find the correct options for each question as following.

Q: 3. sin(x+5) = -0.25 xE [-7,15] (answers to 3 decimal places)

A: The given question can be solved as shown in step 2.

Q: 7 (1 + sin² x) = e 2" sin 2.x, y(0) = 1 X 7) dx

A: This equation solve by separation variable

Q: 9. cos (2t) dt 10. " sin?t cost dt /2 11. sin'x cos?x dx 12. (2 sin0)² d®

A:

Q: (d) r(π/6 + At) - r(π/6) = √3 2 cos At sin Ar-1+(cos Ar i+ At + 2 3√3 2 -sin At 1 3/-)1 2 X

A: We can solve as follows

Q: 10. Solve for t on the interval [0, 2π) (a) 2 cos² t-cost-1=0 (b) 2 sin²t-3 sint + 1 = 0 taol al (c)…

A: Given

Q: | cos(2) sin*(x) + 4 cos(x) sin(æ) + 4 cos(r)dx =, In the above equation an unknown substitution u…

A:

Q: 6. sin x (1 + sin x cos x) dx y csc² ( tan (y²)) dy 7. cos²(y²) sec (11w) tan (11w) V (2 – sec…

A:

Q: B sin 5x+ sin 3x 1 sin 5x+-sin 3x+c 6 I 10 fcos 4x cos.x dx = ?

A: Given :∫cosxcos4xdx

Q: fe* cos (2x) dx A. B. C. D. 2e* sin(x) + 2e* cos(x) + C 2 2 ex sin(x) ex cos(x) 2 2 2 ex sin(2x) ex…

A:

Q: 5. y + 4y= sin x + 3 cos x Ans: y = C₁+C₂ cos 2x + C3 sin 2x + sin x x-co COS X

A: To solve the given differential equation.y'''+4y'=sin x+3 cos x

Q: 1. Given sinx 12 and cos y : 13 both x and y lie in sxs, determine a) cos(x+y) b) sin 2y

A: Given query is to find cos(x+y) and sin2y.

Q: Need help with these

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Q: Solve for x where 0 <x < 2n. a) cos (a + ] V2 sin æ b) 5 cos? x – 13 sin x +1 = 0

A: a) The given equation is cosx+π4=2sinx. Solve the above equation as follows. cosx+π4=2sinxcosx…

Q: Find the general solution of y''+ y =1/cos x

A:

Q: 5. Find the PARTICULAR SOLUTION: y' = 1+ 3y tan x when x = 0 ; y = 1

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Q: 9. y"+y= sec² x Ans. y= c, sin x + c2 cos x0 + (sin x ) In(sec x+ tan x)–1

A: Let's find.

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.