Find anti deriva tive Fa) of the function, an foal- fxl = 5 sinx such that Flo) = 8+ cosX

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

A: Given:sinx=0.3

Q: Prove the following  (sinx)(secx)(cotx)= 1

A:

Q: the Area that lies inside r=3+2 sin 0 out side r=2 is

A: Given: r=3+2sinθ outside r=2To find: AreaNow, 2=3+2sinθ…

Q: Prove that cos(sinx) = /1 – x².

A:

Q: Find tue indefinike insegred. Jcostex) sin'ces) de 3 6 (os (2x) Sin

A:

Q: (a) Buktikan, Prove that, (sin x + cos x)* = sin" 2x + 2 sin 2x + 1. %3D

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Find tano $+ SinØ

A:

Q: L[sin bd]- show that

A:

Q: The smallest positive number for which sin(2z) sin z = 0 is z = Hint: Apply a multiple angle or…

A: Given information: sin2x-sinx=0                                          ...(1)

Q: What is the integrable form of sin-cos-sin@ de? 2 2 sinu du cosu du

A:

Q: Where are the theta valuss for the horizontal and vertical tangent lines on [0,2pi) of r=1+cos theta

A:

Q: Exer. 11-16: Express as a trigonometric function of one angle. 11 cos 70° cos 53° + sin 70° sin 53°…

A: Use the trigonometric identity cos(a-b)=cos acos b+sinasinb where a is 70°and b is 53°. cos 70°cos…

Q: Use an appropriate substitution and then a trigonometric substitution to evaluate the integral. 9+x…

A:

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

A: To Prove1−sinx1+cscx=cosx×cotx

Q: find show that Q Coshz =CoshX Cosy+isin hx Siny

A:

Q: Show that cosh iθ = cos θ,

A: We know that  coshx=ex+e-x2 and by Euler's theorem, eix=cosx+isinxe-ix=cos-x+isin-x=cosx-isinx We…

Q: Prove the following Tanx+secx=cosx/1-sinx

A:

Q: Find the areg between Ye CosX an d y--SinX trom o tr .

A:

Q: esirq) . cos(q) dq 5x/2

A:

Q: sinx + 1-cotx cosx sinx + cosx 1-tanx

A: We have to prove the given identity: cosx1-tanx+sinx1-cotx=sinx+cosx

Q: Show that Cosx dx 9- Sin 3D

A:

Q: Exercise 3. Show that (a) sin z = sin z: (b) cos z = cos 7.

A:

Q: Prove the identity. cosx sin (x+y) – sinx cos (x+y)= siny

A: In question We have given two identities and we'll prove it, (i). Cos(π + x) = - Cosx  (ii). Cosx…

Q: Determine the value of  tanz if sinz + cos z=0.2 and pi>z<pi/2

A:

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

A:

Q: Show that cos( arctan( sin( arccot(x)))) = sqrt{{x^2+1}/{x^2+2}}

A:

Q: What is the value of the i in the ex

A:

Q: 6. Use the identities to find cscx and cotx if secx =7 and sinx < 0. Show all work.

A: Solve question number 6 as asked by the user .

Q: Verify Rolle's theorem for: f(x) = e*(sinx - cosx) on

A: Given:

Q: cos(Inɔx),>o

A:

Q: Prove the following 1/tanx+cotx=sinxcosx

A:

Q: Show that the following statement is true by transforming theleft side into the right side. cos…

A: We have to prove the statement: cos θ tan θ=sin θ We know that tan θ=sin θcos θ

Q: What is the integrable form of sin-cos-sine de? 2 2 (A) - - B -2 sinu du (D cosu du

A:

Q: Prove the identity. csex- sinx cotx cosx

A: csc(x) = 1sin(x) cot(x)=cos(x)sin(x) sin2x + cos2x =1

Q: Prove that osIl" + sini = tan s 56° cas 11-sinll %3D

A: -To show:cos11o+sin11ocos11o-sin11o=tan56oBasic formula needed:-tan(A+B)=tanA+tanB1-tanA.tanB…

Q: & tan B give

A: We have to find

Q: Use the addition formulas to deriv TT 31. cos(x - sin x 2

A: Prove that cos( x  - π/2 ) = sinx Here we use general formula : cos( A - B ) = cosA×cosB + sinA×…

Q: 2. Prove the following identities: a) tanx + cotx = secxcscx cosx + 1+sinx cosx b) 1-sinx cosx

A:

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

A:

Q: (폭), Let f (x) = x5 sin- Then %3D f'(x) =

A: Given that, fx=x5arcsinx27To find f'(x)

Q: find the intergral of f(x) = sin(x) + cos(2x) on the interval [0,pi]

A:

Q: Find the Valve of నలాకె Sin

A:

Q: Prove the identity. sin 2x cotx %3D 1- cos 2x

A:

Q: Q4: Prove that: secx * cscx = tan x + cot x %3D

A:

Q: Xx sec( 2x

A: Solution:-

Q: S- cos ve ve sin? ve de =

A: We will evaluate the given integral.

Q: Define Rolle's Theorem. With the help of Mathematica, show the applicability of the theorem en…

A: Rolle's Theorem: Let a &lt; b If f be a continuous function on the closed interval [a, b]  and…

Q: Use an appropriate local linear approximation to estimate the value of sin(31°).

A: