By the samc way, prove that g 7 sinw.k MUIS Z N-27 cesW. +1

Q: Ao/ prove JhaT cosh(2i4ze)= Coshzi coshde + Sinh 2,Sn hze

A: The main objective is to prove that coshz1+z2=coshz1coshz2+sinhz1sinhz2. The following formulae are…

Q: Let csct = V5,t e QII Find sin(2t) 4 O 2 V5 V5 25

A:

Q: b. Prove that 2cot (20) = cot(0) - tan(0)

A: To prove the identity.

Q: Tan Be Xe O de d Bo find

A:

Q: d) Using Demoivre's theorem, show that, if z = e“, then i(:-" - ") sin no = ne N+ 2

A:

Q: Ex 15: Prove that : d du tanh u = sech2 u dx dx Proof:

A:

Q: If n is an odd natural number prove that I =, xsinnx dx = sinx 2.

A: Consider the given: It is given that n is an odd natural number, Take n = 1,Substituting n=1 and…

Q: Show that coshr + sinh r = e" and cosh r - sinhr = e. Hence, deduce M MOUTMOUT cosh? a – sinh? r 1.…

A:

Q: cosh? z + sinh2z=1 true False O оо

A:

Q: Q: If cosece - sin e = t and sece - cos e = m, prove that l'm? (12 + m2 +3) =1 1. %3D

A: Given that cosecθ−sinθ=lsecθ−cosθ=m

Q: i) um asinx-sin2z ,u fünute, fünd the vaue the uimit. tana ofa and

A: Now, the limit is finite given so, the above must be 00form So,  a cos0-2cos0=0⇒a-2=0⇒a=2

Q: if y=tan x,prove that y'''=2(1+y²)(3+y²)

A:

Q: -W : By the same way, prove that g Z sinWo sinw.k Z -27 cus Wo +1

A:

Q: Tet z. tan Z. tan x X= u cosV, y: usinv find 23 and

A:

Q: if it was fcx) = Sin 3X,9(x)=COS4X EC where the internal multiplication is ove katati ID =S fcx) gx)…

A: f and g are perpendicular when , <f,g> = 0

Q: Q6:-Prove that: y" = 1 if y=;csc (tan"

A:

Q: Show thatI cos ve (-1/4s)

A:

Q: Jósec? 30/3+2 tan 30d0 8.

A:

Q: For z C, show that the solutions of cosh(z) = 1 are z= i2km, for ke Z.

A: We need to prove that the solutions of the equation: cosh(z)=1 are z=i2kπ, where z∈ℂ, k∈ℤ.

Q: Prove the left side equal to right side in the following: s2 (eice = (sin at + at cos ar] 1 L-1 (s²…

A:

Q: Iff (x) = x sinx, thenf' (x) = ? O xsin(2 + x) O 2rsinx O xcos(2 + x) O 2xsinx +xcosx Oxcosx

A:

Q: In A XYZ, ZZ is a right angle and mZX = 53°. Which statement is true O cos 53* YZ %3D XY XZ O tan…

A: From the given figure representative diagram is shown below:   With respect to ∠53°.…

Q: what is Selution of DE (D-20)Y=ê Sinx When Sotved using the meth ed of undetermind

A:

Q: dz dz Find Ju when u = In 2, v=5. if z = 20 cot 'x, and x= e" + sin v. and dz (Simplify your…

A:

Q: V3 Prove that sin 10° sin50° sin 60° sin 70° %3D 16

A: Given, sin10.sin50.sin60.sin70 =sin 60.sin10.sin50.sin70 = [(√3)/2]sin10sin50sin70 =…

Q: prove the following identy (sect − sin(π/2 − t))(sec(π/2 − t)−sint) = tant − tantsin2 t

A:

Q: Te 2=tnx then prove thot dx 28 Snメー tty? 1+xて

A: We have to use proper calculus applications.

Q: Sinex dx is a) Conv. to o 6) diverge b) cont. to 프 auou (P

A:

Q: If y = tan x, prove that y``= 2(1+y² )(3+ y²).

A:

Q: erify that they satisfy al ar argument sin(m - 1

A:

Q: Show that the following cosh 3 (0,0) r(3,5) x² y?. (10xdx +6ydy)

A:

Q: a2z a2z dz Q3) A: If e-(sinx + cosy), show that ax2 ду? at

A:

Q: If y= tan x , prove that y`= 2(1+ y² )(3+ y²).

A:

Q: Nhat is Duf at P(1, 1) if f(x, y) = sin(x - y) and u=i-İ? 3 O 5 O 3 4 O 10 9

A:

Q: Ifcesese - sin e = t and sece - cos e = m. prove that 1'm? (12+ m? +3) =1

A:

Q: that V2- Vz sin 22.5° %3D 2 n exact expression for the indicated quantity. 2.5° %3D Edit

A:

Q: EXpress ume trig fatIOS as TTACCTIOTIS TII Smmpiest teTIIS. 16 R. V33 17 sin R = Cos S sin R and cos…

A:

Q: xsinnx I= dx = 2 sinx

A: …

Q: Suppose you Know that tand 3/12. Vsing this infe, de tevmine cuhot quadiantdis in dnd Caliulate…

A:

Q: TL 3. sin²4ycos²2ydy T

A:

Q: Let fla)= é cosx, s** %3D Express your answers in exact form.

A:

Q: a²z If z = arctan ), find ( ay?

A: Given,           z=arctanyx= tan-1yxTo find           ∂2z∂x2+∂2z∂y2=?

Q: use the definition, prove that d sin z = cOs z dz

A: Topic = Derivative

Q: V- Assuming Cov(X, u) = 0 allows us to equate Ex û to zero. True or False? Explain.

A:

Q: Given that sin x+y3=ax2y, express y' in terms of x and y.

A: Objective is to find y'.

Q: For u = ex cos y,(a) verify that ∂2u/∂x∂y = ∂2u/∂y∂x;(b) verify that ∂2u/∂x2 + ∂2u/∂y2 = 0.

A: The given  function is, u=excosy (a) To verify ∂2u∂x∂y=∂2u∂y∂x Solution: We have u=excosy…

Q: Find all Solotioms Cin radins) to the eguotion 2 Sin X+V3= o

A: