sin^2 x + sin x cos x over cos x − 2 cos^3 x

Q: sinx 4 COS x cos*. COS x

A: In this question, the concept of Integration is applied. Integration Integration is a method of…

Q: L’Hôpital’s Rule is used incorrectly. Describe the error.

A: Given: limx→∞xcos1x

Q: y = tan(x sin x) O (x + sin x) sec² (x sin x) O (x cos x + sin x) sec² (x sin x) O (x + sin x) sec(x…

A:

Q: ∫sin(8x)sin(x)dx

A: Solution:- =∫sin8xsinxdx Applying the Product-to-sum formulas,   sinxsiny=12[cosx-y-cosx+y]…

Q: c) cos x tan x = sin x tanx %3D (Usx.SinzL (os x Sinc sinx cot x + = csc x - CSC X 1+cos x (e Sinzx…

A:

Q: •sin ² (x/2) = = (tan x sin x)/ 2tan x = sin ² (x/2) •tan x - cot x = - 2cot 2x •sin ² (x/2) = (sin…

A: 3) sin2x2=sinx tanx22=sin2x2 4) sin2x=2cos2(x/2)1-cosx=sin2x 5) 2sinx-sin2x/(2sinx+sin2x)=tan2x/2

Q: VERIFY THE IDENTITIES

A:

Q: Verify the identity.

A: To prove - sin2x+sin6xsin2x-sin6x = -tan4x cot2xProof - Taking left hand side of the given identity…

Q: (csc x- cot x)2 = 1- cos x %3D 1+ cos x

A: To prove: (csc⁡x−cot⁡x)2=1−cos⁡x1+cos⁡x We know that csx = 1sinx, cotx=cosxsinx

Q: 3. lim X-0 sinx sinx-cosx 4. lim x- 5. lim x(cosx-1) sinx-x

A:

Q: 3(cos a- 1) sin x cos – sin x O 3 cotx+3 csc x O 3 tanx+3 csc x O 3 tan x +3 sec x O 3 cot x +3 sec…

A: Here we have to find the value of    3(cos2x -1)/(sin x cos x - sin x)

Q: sin'x+ cos x sinx 3 ,2. tan x sec x = 2 cos"x

A: use simple trigonometric relations to prove it.

Q: sin (x) – cos²(x) Show that 1 F COS %3D CSC (x)

A:

Q: Verify the identity:

A: The given identity is 1+sinx1-sinx-1-sinx1+sinx=4tanxsecx

Q: sen x = 0,5 cSC X =. V3 cot x = tan x = cos x = -3 X = sec x = tan x = - /8 cot x = -5 cos x = sec x…

A:

Q: sin(2x)ln(sin²x+1) iv. (sin²x+1)

A: Given:    ∫sin2xlnsin2x +1sin2x +1 dx

Q: Use identities to simplify each expression.

A: cosxsin2x+cos3xsecx=cosxsin2xsecx+cos3xsecx=cos2xsin2x+cos4x…

Q: sec x sin x sin.x Cosx 1 – cosx sin x sin.x 1- cos.x

A:

Q: sin 2 x + sin x + cos 2 x - 1 = _______ tan x cot x sin x cos x

A: We can solve it as below.

Q: sin x 1+cosx 2csc x= 1+cos x sinx

A:

Q: sin(cosx * x + Vx) (cosx)2 sin (x²) * cos(x –-) sin(x) – 2

A:

Q: sin 2x 4. tan x = %3D 1+cos 2x 19 5. tan %3D = CSC X - cot x

A:

Q: (sin x + cos x) sin'x- cosx sin'x- cos'x cos-r COS X (sin x – cos x)2

A:

Q: inx-cosx -= sin x cos x сх-sec x сot х 1 cotx cscx+cotx tanx < – sin*x = 1 – 2 sin² x cot x sin x…

A: According to our guidelines we can answer only three subparts, or first question and rest can be…

Q: sin x COsx Prove 2tanx secx - - cosx 1+ sin x

A: We use the identity sin2x + cos2x=1

Q: tan x -cot x sin x cos X %3D tan2x-cot2x 1-sin x %3D 1+ sin x 4. (sec x- tan x)² 3.

A: 3)tanx-cotxtan2x-cot2x=sinxcosxL.H.Stanx-cotxtan2x-cot2x=tanx-cotxtanx+cotxtanx-cotx=1tanx+cotx=1sin…

Q: sin x COS X Show that secx = then use the identity to derive the basic integration rule sec x dx =…

A:

Q: sin x = csc 2x cos x cos 3x sec 2x

A:

Q: sin 2x + sin x + cos 2x - 1 = _______ cos x cot x tan x sin x

A: Solution ) sin2x + sin x + cos2 x - 1  = sin2 x + cos2 x + sin x - 1 We know that  [ sin2 x + cos2 x…

Q: (sin x + cos x)dx sin² x sin 2x sec x dx sin 2x dx 2 sin x cos² x

A:

Q: sinx 0 cosx –sinx cosx is non singular for all values of x. 1 lect one:

A:

Q: tan(x) - cot(x) = sec(x)(2 sin(x) – csc(x)) %3D tan(x) – cot(x) sin(x) cos(x) %3D cos(x) sin(x)…

A: We can use the trigonometric identities, sin2x=1-cos2x,  cos2x=1-sin2x tan x=sin xcos x, cot x=cos…

Q: (Sin X-cos X)^2=1-sin 2x

A: Formulae to note: (a-b)2=a2+b2-2ab. 2 sin x cos x=sin2x. Sin2x+Cos2x=1.

Q: cos(x (*). cos(x + h) – cos x cos h – 1 sin h - - sin x · h COS x h h

A: Require to verify the identity cosx+h-cosxh=cosxcosh-1h-sinxsinhh

Q: integral sin6(3x) dx

A:

Q: sin 7x dx 1 1 sin dx x cos² x 2 | (tan x + cot x) dx

A:

Q: Integral of Sin^5 x dx

A: We need to find We know that

Q: / Vtan(x) d.x sin(2r) I Vtan(x) -dx sin(2x) -d.x sin x cos x /cos x 2 Multiply by something that is…

A: We have to find integration

Q: 4. (tanx)(1 - cot x) = tan x - 1

A: Given  (tanx)(1-cotx)=tanx-1 Let's verify the identity as shown below

Q: cos'x - tanx 5. prove it cot'x - sec'x sin'x 1+ sec x 6. sin'x sec x 1- cos x cosx 7. 1- sin x cos x…

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Q: coS x cotx cos x-sin x cotx -1 II

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Q: Integral of sin^4 (x/2) cos^2 (x/2 dx

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Q: tanx(1+cot^(2)x)=(1)/(cosxsinx

A: To prove tanx1+cot2x=1cosxsinx consider the left hand side  tanx1+cot2x=1cosxsinx we know that…

Q: tanx – lim 0 Cos[1 – –

A: Given, -limx→0cos1-tanxx

Q: 1- Sinx+ Sin'x 4 X. 2 1-Cosx+Costx 1- Sin'x (1- Sin²x) (x, 1-Cos'x (1-Cosx)

A:

Q: sinx + sin 2 Evaluate | cosx A. -In cos x|– x+ C В. In'secx-x+ C C. -In|sec x|+ x+C D. In sec x|+x+C

A:

Q: sin 3x-sin x 5. cos 3x+cosx tan x

A: Definition used -…

Q: sin(3x)-sin x - cot(2x)= cos(3x) - cos x

A:

Q: sin x cos x 1 1. - sin – sin x 2 sinx cosx 3 cosx -1

A: The solution is given as

Q: sin x-cos x 1. tan x csc x-secx cot x sin x cos X 1 1 2 2. cscx-cotx cscx+cotx tan x 3. cos4x - sin4…

A: 1. sin x-cos xtan x csc x-sec x cot x=sin x cos x2. 1csc x-cot x-1csc x+cot x=2tan x3.…