1) Find thesexact value o niSinG/2) ban sin x Ei Joven that 4 2.

Q: ) Prove cot 2 = tan u using the addition/subtraction formulas.

A: Given : cotπ2-u= tanu

Q: 7. Prove that: (3) (a) (4) (b) sin20 cos20-1 in (-0) + cos (- 0) = cost -cote =

A:

Q: If sino + sin'0 +sin' 0 = 1, then prove that cos 0-4 cos* 0+8cos 0 = 4.

A: sin2 x + cos2 x = 1.

Q: Apply Maclaurln's Serles to Show (-1)*-1,2=-2) 2(n – 1)1 cos X=

A:

Q: 2) DISCUSS The Contmuyo f Sin TX %3D

A:

Q: Prove that cos(sinx) = /1 – x².

A:

Q: Find he principal valeier of the folousag (@) tanG) (6) Cos ) co tan 62) चिम्य ख

A: Given: tan-1-1, cos-112, tan-13, cos-1-12 we know that tan-1-x=-tan-1x…

Q: Suppose that sin(θ)=4/8. What tan(θ)=______.

A:

Q: 11. Use the substitution u = x/3 to prove dx tan 9+x2

A: Consider the integral

Q: (1) Use Simpsons 1/3 rule to find sinxdx

A: Topic:- Simpsons 1/3 rule  Note:- if more than one question uploaded than only first question need…

Q: a) Buktikan, Prove that, (sin x + cosx)* = sin 2x + 2 sin 2x +1.

A: The given equation,sinx+cosx4=sin22x+2 sin2x+1

Q: =-i In (izt Ji-z2?) Sin 군 tan 군 = 늑In

A:

Q: Find the exact value of sin 5π/12 using the fact that 5π/12 = π/6 + π/4.

A:

Q: Find the Integrationof {(u) = tanu + Cos 24. %3D

A: Consider the function, fu=tanu2+cos2u

Q: Show that sin 3x and cos 3x are orthogonal on [−π, π].

A:

Q: 2 _ 2 if tane + sin0= m and tan0 – sin0 = n ,show that m² – n´ = 4 mn

A:

Q: tan 6= .and 0s@s90 , then sin 0- O V3 2. V5

A: Solve for sin theta

Q: do sulev tos 11. sin 405° 12. cos 420° 13. tan 405° 14. sin 390° 15. csc 450° 16. sec 540° 33т 19.…

A:

Q: Evaluate fi' sin(21*)dt

A:

Q: Derive the ivenidentitics Sin 20 CoS 20 %3D seco sino COso

A: We have to derive the identity                                        sin2θsinθ-cos2θcosθ=secθ

Q: 5. If coshx = csc20, prove that 0 = n+ cothe¬x. [Hint: use identity sin(2a + 2n)]

A:

Q: Describe the thans formation and tan Station by rephesented by the Pquatlon 9= -2.5 Sin (x - 13.4°)…

A: y=-2.5sinx-13.4°-0.6To describe the transformation and translation

Q: If tan-0 = 1- a Prove that sec® + tam Ocosece = (2- a) 3. %3D %3D

A:

Q: 1. tanxsins + cosx = secx

A: using trignometric identities:-

Q: . Suppose csc(A)· where A terminates in QIV, and sec(B) = -3 where B terminates in QII %3D a) First…

A: Note the trigonometric identities :

Q: Show that V2 + V2 cos 2 and cos 16 and use it to find sin 16 Show that

A:

Q: Suppose that π≤θ≤3π/2, tan(θ)=6/12, find sin(θ)=______. (round to 3 decimal places)

A:

Q: Show that the equation sin(cos 2x)= V1-4x² is an identity. %3D

A:

Q: Show that given that z = sin-12 дхду дудх

A:

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

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: Find the exact value of sin 20 if tan 0 with 0 in QII. 4 %3D O - 8 17 13 17 8 17 17 o 4V17 17

A:

Q: prove that: a- cos20 = cos²0 – sin²0 %3D sin20 = 2sin0cos

A:

Q: Prove the below cos' x sin 3x + sin' x cos 3x 3 sin 4x 4 II

A: Simplification of trigonometry function

Q: Prove that cos 17° + sin17° tan62° %3D cos17° – sin17°

A: Devide the whole left side by Cos17° and use formula of tan(a+b)

Q: Express as a sum.(sin ax)(cos bx)

A: Given : (sin ax)(cos bx)

Q: 3. Suppose csc(A) = where A terminates in QIV, and sec(B) = -3 where B terminates in QII

A:

Q: Q4:B/Simplify [cos 20-i sin20][cos 30+ i sin301² [cos 40+ i sin40³[cos 20-i sin2015 using De…

A: Formula Used-  De Moivre's theorem: cosθ+isinθn=cos nθ+isin nθ cos mθ+isin mθcos nθ+isin nθ=cos…

Q: If cos u = - 2/3and u terminates in QIII, find sin u.

A: Given: cosu=-23, u terminates in 3rd quadrant We know that if u is in 3rd quadrant then sinu and…

Q: Show that sin , +sin ¤, = 2 cos[;(4, – Þ,)]sin[;(P, +Ð,)]

A:

Q: (7) (a) Prove the identity using Double Angle and Sum to Product Formulas: sin 10x cos 5x %3D sin 9x…

A:

Q: If 2 sin-' p = cos-q, show that 4p² – 4pª + q° = 1.

A:

Q: Use DeMoivre’s Theorem to find z4 if z = 2 (cos 3π/4 + i sin 3π/4). Write your answer in standard…

A:

Q: Use Simpson's rule with n = 4 to approximate /" cos(2) -dr

A: Given: ∫16cosxxdx Here a=1, b=6 and n=4  h=b-an∆x=6-14∆x=54∆x=54

Q: Find cos if sin = 1/2 terminates in QII

A: Given data:     The given value of the trigonometric identity is: sinθ=1/2.     Evaluate the given…

Q: Use Figure 7 to prove that (cos- x)': V1 x2 1 V1-x y FIGURE 7 Right triangle with y = cos- x. %3D

A: y=cos-1x⇒x=cosy

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

A:

Q: Prove CotA= sin2A/1-cos2A

A:

Q: Find tan o if sin 0=2/3 and 0 terminates in q1

A:

Q: Simplify [cos 20-i sin2018[cos 30+ i sin301² [cos 40+ i sin40 1³ [cos 20-i sin2015 using De Moivre's…

A: This question can be solved using the De Moivre's theorem which says eix=cosx+isinx