tan y-1 . sin y- cos y- 1 www. Prove that tan y +1 sin y + cos y+1 2.

Q: Evaluate the integrals

A: We have to evaluate the given integrals .

Q: 1 lim h-0 2h sin(x²)dx = %3D -2h O cos(1) sin(1)

A: Using Fundamental theorem of calculus: ∫-2h0sin(x2)dx=sin(0)-sin((-2h)2)=0-sin(4h2)=-sin(4h2)

Q: Evaluate sin(x+y)-cos(x+y)=1

A: Given: sinx+y-cosx+y=1 Dividing both sides by 2, we get  12sinx+y-12cosx+y=12

Q: 1. tan(x + T) = tan x %3D sin(x+y) 2. cos x cos y = tan x + tan y %3D

A:

Q: · y = sin(cos 3x) – sin x cos 3x

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

Q: Differentiate y = sec (x2 + 2) A. 2x cos (x2 + 2) B. -cos (x2 + 2) cot (x2 + 2) C. 2x sec (x2 + 2)…

A:

Q: (2 cos z-sin z)² dx Evaluate sin z

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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: y = sin' x- cos 3 – cos' x cos³

A:

Q: Find y" of sin y + cos x = 1 using implicit differtiation

A: Given Data: Equation: siny+cosx=1 ......1   The first differentiation of equation (1) using the…

Q: 2 + sin x Differentiate Y x + cos

A:

Q: tan 2x sec 2x dx Evaluate cos 2x O 1 ,tan 2x e + C 2 2 e tan 2x + C O -2 e sec 2x + C 1 ,tan 2x + C…

A: ∫etan2x sec2xcos2x dx=∫etan2x sec2x sec2x dx     ∵secx=1cosx=∫etan2x sec22x dx Now put,…

Q: y= sin(x + 4) cos (x - 4) y= sec 4x + tan 4x y= Arctan

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

Q: (1) If y = sin(tan-x), prove that %3D (1+ x²)?y" + 2x(1 + x²)y' +y = 0.

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: cos(x – y) Prove that tan y + cot x sin x cos y

A: We need to prove cosx-ysin x cos y=tan y+ cot x                  Now, we will use the formula…

Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = sin-1 (xyz)

A: Given that f(x,y,z)=sin-1(xyz)

Q: 2) Proof that If y = f(x) = = cos x then dx sin x

A:

Q: (1+ etane) sec² e de = e TO FO 2 [0(sin(In 0) + cos(In 0))] = de csc(ln 0)

A: ∵1     ∫0π4(1+etan θ) sec2θ dθ=∫0π4(sec2θ+etan θsec2θ )dθ=∫0π4sec2θ dθ +∫0π4etan θsec2θ dθ∵∫0π4sec2θ…

Q: tan x (sin xXcos x) 1+ tan x L.S. R.S.

A: Solution of trigonometric Identity

Q: Verify the identity. sin(x + y) – sin (x - y) = 2cos.xsiny

A: To verify the identity, sinx+y-sinx-y=2cosxsiny

Q: y = tan In(x + sin x) %3D y = sin x + In sin e* %3D

A: y=tan ln(x+sinx) y=sinx+ln sinex

Q: 3. y = ln³(x + sin x) 4. y = tan¬1(3x) cos 1 4x G ED DI 5. y =

A: All the questions are a solved below.

Q: sin.x 14. What is y" if y=1-cosx A) y'= B) y'= -COS.X (1 – cosx)? sinx (1-cos.x)² C) y'= D) y'=…

A: Given: y=sinx1-cosx We have to find y''.

Q: (1) (sinz) + (cosr)* sin x COS x (2) tan x in terms of sin x, cos x %3D d. d. ( sin x COS X %3D dx…

A:

Q: 22. y' = 1 + 3y tan x. ANS. 3y cos³ x = c + 3 sin x – sin³ x.

A:

Q: 1 + sin x Differentiate y = x + cos x

A: As we know that: The Quotient rule: fg'=f'·g+g'·fg2 The Power rule: ddxxn=nxn-1 Given:…

Q: C. tan 0 = 3 sin 0 over [0, 2n) %3D

A:

Q: S tan -) dx = a) x tan-1 (-) +÷In(x² + 1) + C b) x tan-1 () +글x2-글In(x2 + 1) + C c) x tan-1 (는) +글x2…

A:

Q: (i) * cos x + cos x tan²x dx sec?x (ii) |x – 2| dx (iii) | x²/x* + 1dx

A: Since you have posted a question with multiple sub-parts, as per the company guidelines we will…

Q: sin(bx)+a x<0 f(x)=< | sin (2x)+2x x20 which is differentiable everywhere, then what are values of a…

A:

Q: 4,5in3x =sinx S Sinx(sin?x-\= sin?x. Sinx(sinx-1). COS X tank (sin zx - COS tan-o TT

A:

Q: (1-cos 6x)dx Perform the integration:S 1+cos 6x tanx - x +C c. tan3x – x+C A. -tanx – x+C D. tan3x –…

A: We have to choose correct option

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: Solve (cos x cos y- cot x) dx-sin x sin y dy = 0 %3D

A:

Q: 5. (cos" x- y cos x) dr - (1 + sin x) dy =0

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: 2) + (2x tan-" y – x³)(1+ y²) = 0 Ans: tan-y=(x² + 1) + ce-*²

A: Bernoulli differential equation in the form of: dydx+k(x) y=q(x) yn 1yndydx+k(x)×1yn-1=q(x)…

Q: 7. (3 tan x 1 - 2 cos y) sec² x dx + tan x sin y dy = 0. ANE cos y tan² y ton3 y L

A:

Q: solve eYsin(x) -y'cos"x = 0 2. cos¯x=0

A:

Q: ) Evaluate antan L tc 2 - arctan -x3 - 2 tc arctan 3- 2) Evaluate dx 5 arctan arctan x*-5 +C 45 -…

A:

Q: 1. Evaluate: sin r dx COS x sin r cos r dr tan r dr COS dx tanx dr 1- sin r

A: Given: To find: The values of integral.

Q: √x(y)²-(√x cos √x - sec √x)y'=1

A:

Q: 3. y³x2 – cos- sin x² + esin x = 1 y DIFFERENTIATE THE GIVEN

A:

Q: a) y=In(*). x tane 4 cos x y = 3x + sinx b)

A: Given: The functions are, a) y = ln ( x tan ex )

Q: at y = ". For cos x – sin y=-, find the value of so that ky'"=-1 at y="

A:

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.

Q: 2. y = tan-1(sin 3x) + cos-(cos x)

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

Q: 04.) Show that y = (sin x +cos x) sec x = sec² x

A: Given inequality does not equal. See the attachment