integrate (cos (x)/(sin(X)-cos(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: sinh x 1+ cosh x

A: sinh x1+cosh x

Q: /1+cos x + V1- cos x X =-+÷,0<x<“ 4 2 V1+ cos x - V1-cos x - cOs X

A: Using trigonometry formulas we solve here given question

Q: lim x approaches zero, sin4x/sin3x

A: Given,

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

A: use simple trigonometric relations to prove it.

Q: cotx(secx-cos x)

A: We have to find  cotx (secx - cosx) We know that ,  cotx = cosx/sinx secx = 1/cosx  Then ,

Q: Sinx lim Cos 1-

A:

Q: sin x 1+ cosx 1+ cosx sin x 2cscx 2secx 01

A:

Q: b) (cosx+ Sinx)² - Cos x+sinx)(cosx-Sinac) tan 2x 2. c) 1-Cos-x - Sin2oc) Sin X - 2cos x

A:

Q: Verify the identity.

A: Use the trigonometric identities sinA+sinB=2sinA+B2cosA-B2 and cosA+cosB=2cosA+B2cosA-B2 to simplify…

Q: T-cosx 2. limx-0 3.limx-0 sinx x2 +1 4.limx-0 x+cosx

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

Q: Use identities to simplify each expression.

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

Q: SIn (-x) In x if x 0

A:

Q: sin (3x) + cos (3x) cos(x) – =1+4sin(x)cos(x)

A: We use sin(3x)= 3sinx-4sin3x and cos (3x)= 4cos3x-3cosx .

Q: 1. sin (-x)(sin(-x) + 1)

A: Given; Sin(-x)[Sin(-x)+1].

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

A:

Q: lim cos2x-1/sinx x-> 0

A:

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

A:

Q: sin x 1+ cosx 1+ cosx + sin x 2cscx 2secx 01

A:

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

A: We use the identity sin2x + cos2x=1

Q: sec x—cscх sin x — сos x sec x•cscx

A:

Q: 8 sin x cos x sec x =

A:

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

A:

Q: secx-secx COS x 2+anx sinx-secx

A: Given To simplify sec x -sec x.cos2 x2 tan x - sin x.sec x

Q: x2 sin x+2x cos x f'(x) = cos²x

A:

Q: integration of sin2x.cos3x dx

A:

Q: cos(2x)– cosx sin x 4. lim, »o

A:

Q: Integration of sin^2 x?

A: Cos(2x) = 1 - 2Sin2(x)  Sin2(x)=1 - Cos(2x)2   Integration of cos(x) is Sin(x)

Q: ifferentiate  y=sin2(sin3x)-(sin(x3+2)/x)

A:

Q: sin x 1+ cosx 1+ cosx sin x 2cscx 2secx 1

A:

Q: ✓cos x lim x 0 1 cos x - -

A: The given limit is limx→01-cosx1-cosx

Q: F CSC'x + - cos2x -cos^x -sec'x

A:

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: 1) f(x) = x5-x¹ + x² - x +² 2) f(x) = sin³x - e³x² + ln(1 + 5x²) 3) f(x)=√1-x² sin-¹ x 4) f(x)=√√x +…

A:

Q: Arcsinx-sinx 1. lim x→0 (1-cos2x)sin2x 2-2cosx-xln(1+x) 2. lim x→0 x sin² x

A: 1)

Q: COs x + sinx COS x - Sln x - sin = 2 tan 2x %3D Cos x- sin x COS x + sin x

A:

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: cos 2x - cos2a Integrate cos x-cosa

A:

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: secx-tanx cos x secx+tanx 1+sinx

A:

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

A: The solution is given as

Q: cos2x – sin2x cos2x - -F(x)+C. What is F(X}? For dr =- 3 cosx – sinx -

A:

Q: 5.) cos (x -) + sin ( – x) = cos x cos (x -) + sin ( - x) = 3

A: Since multiple questions are asked, according to guidelines answering first question. Cos60 =1/2…

Q: sin x cos x tan x = 1 – cos² x -

A:

Q: Lim Sin 2x Sin 2x |- CoS1ox

A: Given: L=limx→0sin2x1-cos10x+sin2x2x

Q: 3 sin³ (tan √x² + 3x²)] dx d [(x²+1) cotx dx 3- cos x csc x

A: To find the following derivatives.i ddx3 sin3tan x2+3x2ii ddxx2+1 cot x3-cos x csc x