de (sin(0) cos(0)) =

Q: sin 0 + In + 22+3 = -3 - cos 20 - In y? + 327-4 = + 2ln y+ 22 -3 1+ (cot 0)2

A: Given system is sinθ+ln1y+2z+3=-3 lny2+32z-4=1-cos2θ2 21+cotθ2+2lny+2z=-3

Q: 9. 2x + cos x = 0

A: We use intermediate value theorem and rolle theorem to show that the given equation has only one…

Q: 1 cos(5x) +... 25 cos(x) + cos(3x) + Ans. + 2 sin(x)+ sin(3x) +sin(5x) +...

A:

Q: · y = sin(cos 3x) – sin x cos 3x

A: Given : Y = sin(cos3x) - sinx.cos3x Let's differentiate:

Q: = 0 If 2 sin x cos x + V2 cos x = 0. 0, then %3D %3D or

A: 2sin x cos x +2cos x=0

Q: 1. ) cos (4) COS -π/2 f/² sin (1) sin (²) dx (Consider initially the first 2 terms)

A:

Q: 1-cos 3x +C dx 1+ cos 3x 3sin 3x

A:

Q: 5. ( sin (7x) cos'(x) dx sin'(x) dx 6. /2 7. cos'0 de 8. Jo sin (20) de

A:

Q: y = sin' x- cos 3 – cos' x cos³

A:

Q: sin(4x) cos(2.x) dx n (2x) sin (6x) cos (2x) cos 2. ()= 4 'cos (2x) cos (10x sin (2x) trts 10 (e)…

A:

Q: 57 sin 6 (똥 + 미) =글(c8 )%3D (cos w - V3 sin w) -

A:

Q: Find , where : = sin (x²) cos (y) COS 6.x sin (a) cos (y) 2.x sin (a) O2.x cos (2) 2r sin (2*) cos…

A:

Q: symbolnc cos(6x) cos(11x) dx = cos(11) sin(6x) + C ncorrect

A:

Q: sin(4x) cos(2x) dx = cos (2x) cos (6x)' sin (2x) cos (2x) сов (10х) 4. (2x) sin (10x)+ c sin +c 10…

A: Use formula 2sinAcosB=sin(A+B)+sin(A-B)

Q: cos

A:

Q: 19. y = -3 cos 2x 20. y = 5 sin 2 AAMA A

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

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

A:

Q: 1-cos 3x +C 3sin 3x dx 2. 1+ cos 3x

A: We have to prove given integral.

Q: 2 cos (x2) - 4x 2 sin (x2)

A: 2 cos (x2) - 4x 2 sin (x2)

Q: 1. ² sin() cos() sin(x) dx (Consider initially the first 2 terms)

A:

Q: 2 cos' xsin* cos° xsin“ xdx

A: To evaluate:∫0π2cos5xsin4xdx

Q: 0 0 1 cos(0) -sin(@)) sin(0) cos(0) 1 1 (a) (c) 0 1 0 (d) -1 | 1 0 0

A:

Q: Im cos 2x + sin 2x} %3D Cos 4i - 4

A: To find: The imaginary part of -x4icos 2x+x4sin 2x. Concept used: If the complex number is written…

Q: 3. у"-2у'— sin 4x 1 cos 4x 40 1 sin 4x 20 Ans. y= c, + c,e²* + -

A: To find: The general solution of differential equation. Given: The differential equation is…

Q: 5. y + 4y = sin x + 3 cos x Ans: y = C₁ + C₂ cos 2x + C3 sin 2x + sinx-cosx

A:

Q: 1+ sin 0 . Verify cos O 2 sec e Cos A 1+ sin A

A: Our Aim is to verify 1+sin θcos θ+cos θ1+sin θ=2 sec θ -(i)

Q: *y=(sin(x)+cos(x))cos(x). dyldx -sin 2(x)+cos*2(x)+2cos(x) -sin 2(x)+cos 2(x)-sin(2x) O

A:

Q: sin(2r) cos(2x) +1 2. Prove: csc(2x) + cot(2r). %3D COS

A:

Q: cos(x) + s(3x)+ 25 cos(5x)+..) 4 Ans. + sin(x)- sin(2x)+ sin(3x)– ...

A:

Q: Cos(5x) cos(2x) + sin(5x) sin(2x)

A: Given: Cos(5x) cos(2x) + sin(5x) sin(2x)

Q: 2 cos x+3 cos x=2 2 Cos²,

A: Given,   2 cos2x+3 cos x=2

Q: 2y 1 + cos 3x - 4.x + 3y sin 3.r = 0 %3D dr

A: 2y-1x+cos3xdydx+yx2-4x3+3ysin3x=0 Rewrite the above ODE in the form of Mdx+Ndy=0.…

Q: 2 2. (sin cos x) = sin 2x +1 2х +

A: The given identity

Q: sin 0 + In + 22+3 = -3 1- cos 20 In y? + 322 - 4 = + 2ln y + 22 =-3 1+ (cot 0)2

A: Given system is  sinθ+ln1y+2z+3=-3 lny2+32z-4=1-cos2θ2 21+cotθ2+2lny+2z=-3

Q: 9. y = -sin (3x) 10. y = tan (x - 60) 11. y = cos (x + 30) 12. y = 3 cos (2x)

A: In both cases there is translation of graph.

Q: 1. f cos³ 3x sin¹ 3x dx 2. fcsc4 5x cot4 5x dx 3. ƒ cos³ xdx from a = 0 to b = 2

A:

Q: y. x -. cos(- + cos(- 2 4 х — у, 2 sin(- 4 = cos x - sin y 2

A: Here, the objective is to prove the following: 2sinπ4+x-y2cosπ4+x-y2=cosx-siny

Q: у%3D sin(4x — 2) cos (4x + 2) || -

A: topic - derivative

Q: Cos (GX) = Cos 15°, 0°<x < 360° Со X) = Cos 15°, O° < x < 360° %3D Tan( x ) = tan,05x < 2n )= tan,

A: We can find the answers as below

Q: •π 2 (sin³r)√1 (sin³ x)√1 + cos x dx

A: Given problem:-

Q: Determine the general solution of y' = cosx cos y

A: we have to find the general solution

Q: 3. x² sin* () dx, x² sin2 () dx, n, n, a is a constant

A:

Q: 3 3m 2. sin ---- sin(20) = b. cos(20) = a.

A:

Q: 2 0 sin 2x dx 3-cos2x

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+siny)[1+sin(-y)]=cos2y

A: Given:

Q: 3 5. cos x dx > 6. sin x cos x dx =

A: According to the trigonometric ratio:  sin2x + cos2x = 1 Integration of cos x is sin x.

Q: * /2 2 sinh (sin 0) cos 0 d0

A:

Q: (sin x)(cos x + 1) = 0 if 0 < x < 2n. А. п/3, 2п/3 В. О, п

A: This question is taken from trigonometry in which we have to find the roots of the given…