H.co/ prove That;. dz 1-2 Cosh2=

Q: Prove that the equation sinx = 0.3 has at least one solution in the interval (o, ~).

A: Given:sinx=0.3

Q: Q1/ Show that 3(sinx-cosx)*+6(sinx + cosx)²+4 (sinºx+cos°x) = 13

A: Note: We are entitled to solve only one question at a time. To Show:…

Q: 41. Show that if u = tanh(x/2), then 2u 1+u? 1- u?' 2du 1- u? cosh x = sinh x = 1- u? dx = Hint: For…

A: To show the following

Q: (5) Evaluate the definite intergral [/³ (sec²x+3x)dx. /3

A:

Q: 10 Use aepropriate substitution Ond then a trigonometric oubtitution to evaleiate the integial. dx…

A: This question can be solved using the concept of integration by substitution.

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: Compute : exp(i sin(e¬ni)).

A:

Q: s nip

A: Given z=tanα2

Q: ) Prove that 2+sinZA Cos A-SinA

A: To Prove: cos3A-sin3AcosA-sinA=2+sin2A2

Q: Integrate sin" uelog(cosu) . Where n=666

A:

Q: Q4: Prove that: (1- sin x)(1 + cscx) = cos x* cot x %3D

A: To Prove1−sinx1+cscx=cosx×cotx

Q: find @ Sin 2TTH Sin 4TTH lt 2. 0.7073in21t icdt

A:

Q: . Evaluate sec z tan zdr

A:

Q: Prove the identity.   (cosh x + sinh x)n = cosh nx + sinh nx  (n is any real number)

A: The cosh x and sinh x are given by, LHS =

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

A:

Q: Find the indefinie intgrel wite 5 sec (2x) tan (2x) dx

A: Topic = Integration

Q: cos" xdx :0. 6. If n is a positive odd integer, prove that

A:

Q: Prove the following equation : Cosh(3 x) = 4 cosh³(x) – 3cosh(x)

A:

Q: కషిద్టి చవీ / tangent s lope rosin (20) when Jot 5 2) 653 3. not of the above

A:

Q: Prove | cosz |2 = cos²x+ sinh²y.

A: To Prove: cos z2=cos2x+sinh2y

Q: By Cauchy's integral formula show that, Se" esin e -2n cos(cose) de = 2n; "esine sin(cose) de = 0 0,

A: Cauchy's integral formula : Let U be an open subset of the complex plane C, and suppose the closed…

Q: E prove that = - Cotx + C %3D 1- Cosx +Sin'x

A:

Q: Find the first 3 Zerms o Sinx et a =?

A:

Q: 7. Integrate. S tan50 sec³0d0

A:

Q: Compute : exp(i sin(e-i))

A:

Q: 46 a Show that cos x+ =-sinx. = -sinx. d" (cosx) = cosx + drn b Prove that

A:

Q: 2. Use the Newtons method to find the root of x-cos.x=0 correct to 3 decimal places starting with x…

A:

Q: Integrate sin" uelor (cosu) . Where n=540

A:

Q: Use the addition formulas to provesinh(2x) = 2 cosh x sinh xcosh(2x) = cosh2 x + sinh2 x

A: Our Aim is to prove the following identities:-(a) sin h(2x)=2 cosh (x) sinh (x)Proof⇒Since, sinh…

Q: Evaluate the in tegrol : S sin 5x cog3 5xdx

A:

Q: Assuming that |a| < 1, find the value of cosh ax dr. cosh x

A: It is given that,a&lt;1, we have to find the value of              ∫0∞coshaxcoshxdx

Q: Prove that the equation sinx = 0.3 has at least one solution in the interval(o, π/2).

A:

Q: HW /Prove that: (1) tanx=cot

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

Q: Prove the addition formula for cosh x given by cosh(x + y) = cosh x cosh y + sinh x sinh y.

A:

Q: Prove (05t - sin 4t tos?t

A:

Q: 7. B- Show that: (1) lime-0 tan 8 (2) tan 0 sec20 =D1 %3D do

A: Solve

Q: @H-w/ prove that cosiz=coshz

A: We have to prove by using cosiz and coshz formulae.

Q: 2. Apply appropriate trigonometric substitution to compute the integral 1-4x +2 dx /2x

A:

Q: 3. tane de ) 71+ n cose)/3

A:

Q: Find a series of cosines of multiples of x which will represent (x sinx ) in the interval (O, x) and…

A: Let's expand x cos(x ) , xcosx=x1-x22!+x44!-x66!+...=x-x32!+x54!-x76!+...             in 0,x To show…

Q: find the area of the limacon: r = 2 + sinx

A: To Determine: Find the area of the limacon:

Q: Find S(3/(x) + cos7x + 4 + 20) dx None x1.5 sin7x + 4log x + 20

A: Now,  We will find the integration to the given problems.    Integration of cosec2x dx = - cot x +c

Q: 2* csch (2*) cosh(2*)-sinh(2*)

A:

Q: 9 Prove Sen 4t 4 cos3t sint-sin3t cos t.

A:

Q: sec 1.)S Intanßtanß dß

A:

Q: E prove that - Cotx + C 2 |- Cosx +Sinx

A: Solve the integration

Q: 14) Show that Cos e= 1- Sino COs o : |-Sinie

A: Given, cos2θ = 1-sin2θ We have to show that.

Q: 6. Show that in the interval (0, 7) 4 cos 2nx sinx = 元 Σ 4n2 -1

A:

Q: B.Determine the values of n and h required to cprovimate sin3xdx to within 0.0002. Use Composite…

A: Error in calculating the integral I=∫abf(x) dx by using composite Simpson's rule is given by…

Q: Show that 1 − cos x = x2/2 with an error less than 0.003 for |x| &lt; 1/2.

A: Given: 1-cos x =x22;    |error|&lt;0.003Formula:  The…