tan x + i tanh y 1- i tan x tanh y 18. tan z = tan(x + iy)

Q: 1. cosh z= cosh x cos y + i sinh sin y sinh z = sinh x cos y + i cosh x sin y.

A: According to our guidelines we are supposed to answer only one question, since you have asked more…

Q: 1. y = sin(x) tan(x) 2. y = cos (x) 3. y = cos(tan(x)) 4. y = tan(x) A. y' = -3 cos (x) tan(x) В. у…

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

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Q: f(x) 3 cos x 2 tan x - - f'(x) = f' 3 r()-

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Q: J 1 cot³ x O 3 2 dx = In | sec² x − 1| + C --- O 1 tan² x + ln | sec x + C 4 O 1 2 O 1 2 1…

A: I have stated the used formulas in the solution

Q: 1. sin (5x + ) sin ( x + T /2) %3D 2. tan (3x – T/2 ) = cot 2x 3. COs (x + п /2) sin ( T /2 – 2x )…

A: Given that three trigonometry equation  To find fundamental solution of the question

Q: y" + y = 2 cos x – 2 sin x; y=x sin x + x cos x y" +y = sec x; y = x sin x + (cos x)In(cos .x)

A: We have two methods two check whether given function is solution of differential equation or not  i)…

Q: sinh (iz) = i sinz sintiz) =isinh z,escia)= cosh: 2. !!

A: In this question, the concept of a trigonometric function is applied, Trigonometric Function The…

Q: 1+ sin x 1- sin x 21. 1- sin x 4 tan x secx 1+ sin x sin (x + y) sin (x - y) tan x + tan y 22. %3D…

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Q: |tan' x.sec x.dr = tan x +C %3D

A: This question is based on indefinite integral.

Q: Prove the reduction formula

A: To prove: ∫tankx dx=tank-1xk-1-∫tank-2x dx

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

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Q: ..LH.S.-R.H.S. - HW/ Prove that: (1) 1-tanh x=sech'x

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Q: 1. If z=ln (x-y) +tan (x+y) find zxx and zyy

A: Given: z=lnx-y+tanx+y  ……1

Q: of of +y y Let f(x, y) = x$y² tan Then x equals X

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Q: S(sec x tan x – 9x³)dx =. - - sec x – x+c O sec r + x° +c O tan x + x +c sec x + x° + c sec 2 — 29 +…

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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: Test for homogeneity 3. f(x, y) = tanx - sec²x - cosy 4. f(x, y): x²+3xy

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Q: 1-T= 3- Z= +cos(y)tan ( √x-b cos (n) 2-sin²(n) 2-B=sin(x) sec(x)/cscf(x) 4-(w+n)²(a+) x-3

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Q: d -tan(z) = dz sec(x) O cot(x) O sec2(z) O

A: we have to find ddztanZ i.e we have to find derivative of Tanz with respect to z ddzTanz=sec2zdzdz

Q: Antiderivative of sec(3x)tan(3x)

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Q: 4) f(x) = V1- x² sin-(2x + 1). %3D y 5) tan(x - v) =

A: As per guidelines we have to solve one question  Please repost other questions again

Q: ation (1+xcos 2y)dr-x'sin 2 ydy = 0. %3D

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Q: Graph each function.

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Q: (sec2 0 – sin 0) de sec y (tan y – sec y) dy 1 2

A: Given:- 1. ∫(sec2θ - sinθ)dθ2. ∫secy(tany-secy)dy

Q: salvepE tany= Sin(2 +y) +Sin(x-y) (ans. secy= C-2 Casx)

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Q: S(sec z tan z – 3z²)dz -secz – z³ +c sec z + x³ + c sec - * +с tan z + 1³ + c O - sec z + z° +c

A: Use integration rules

Q: sec (0) J de 5-sec2(0)

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Q: tanx - tany = sin(x+y)/cosxcosy

A: The given identity to be proved is,

Q: Find y' given that y - y' sec²√x tan√x √x y' = 2sec√x tan² √x y' = 2tan√x sec² √x sec√x tan√x y' √√x…

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Q: tanx If f (x) = A (В) (ⒸC) D - St 0 sec 3x 1+ e tanx In (secx) √ 1+tan ²x 1+ e tanx sec²x 1+elanx…

A: Finding the derivative of the integral

Q: i. y = sinh-1 (x), ii.y = cosh-1 (x),x > 1 iii.y = tanh-1 (x), |x| < 1 %3D

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Q: tanx If f (x) = A B C D f √1+1² 0 1te¹ In (secx)√1+tan ²x 1+ e tanx 1+tan²x tanx 1+e sec 3x 1+ e…

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Q: sec x dx. Vtan x Calculate 2/tan x + 2 (Vtan a) + C O sec 2/tan x + C 3 O 2/tan x + 5/tan x + C O…

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Q: x+y %3D 21. Prove that tan-x + tan-'y tan - xy.

A: Using tan(A+B) =( tan(A) + tan(B) )/(1- tan(A) tan(B) ).

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…

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Q: tan z + sec r - 1 tan z + sec r tan z - sec r+1

A: Given: A trigonometric function tan x+sec x-1tan x-sec x+1=tan x+sec x Simplify LHS first. Multiply…

Q: lim 0 2 + sin(okr }) k=1 6 O A. J(x + sin(2xx)) dx 6 O B. J(2x + sin(2xx)) dx 3 O C. J(x +…

A: Definite integration limit as sum

Q: // dydx O Lan- Lan y sin x .5 kan (x/ 2) ** t e tan (x/2) sin x 0.5 1 sin x .5 tan (x/2) ** y 2 tan…

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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: 6 ý x In x=y 2/y-1 (も 2y=y cotx

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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

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Q: sec (In x) + sec2(In x) tan(In x) dx Given: 2x Find: du

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Q: Prove that sinh z = sinh x cos y +i cosh r sin y.

A: To prove, sinh z = sinh x * cos y + i cosh x * sin y

Q: separable 9-X(2lnX+1) Sin y+ ycosy

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Q: Find y' of sin(x+y)=x+y

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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.