3- Represent in the form of x+ iy a) V8 (cos + i sin m) b) 6 (cos 7 + i sin7)

Q: 4. Establish the identity: sec ar - secr sin2 = cos LIC HS O6Y

A: Establish the identity

Q: a. Express x = --3-8ż in its trigonometric form r (cos(0) + i sin(0)) with 0 ≤ 0 < 2. Give your…

A: a) x=-3-8ib) 2+5i2+2i

Q: Q4:B/Simplify [cos 40+ i sin40 1³ [cos 20-i sin2015 using De Moivre's theorem?

A:

Q: Find the exact value of cos2 15° - sin2 15°.

A: We have to find the exact value of cos2 15°-sin2 15°Formula used :-Cos 2θ= cos2 θ-sin2θ -1

Q: 57T then 4° If 0 %3D - sin(0) equals cos(8) equals tan(0) equals sec(0) equals

A: Using trigonometrical identities.

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: What is the exact value of 2sin(x/2) * cos(x/2) if sin of x = 3/5 and cos of x = 4/5 ?

A: To determine the exact value of the expression.

Q: By using Cauchy laws find: sin (2) dz -i2 cos (2) dz 2-T3

A:

Q: 2n sin(30) do 4. Jo 5+cos²(0)

A:

Q: Prove the trigometr 1-Cos (o) Secco) I +seclo) Sina co)

A:

Q: Find z5, if z=2(cos π/3 + i sin π/3) and onvert answer into rectangular form.

A:

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: B. With the indicated conc the given equation. 2. 2 Cos2 0 = -3 Sin 0, 3. Tan? x- Secx = 1, 4. Cos…

A:

Q: Prove a (cosa + cosß) + (sina + sinß) = 4cos² (@ - B) 2 %3D

A:

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

A: Consider the function, fu=tanu2+cos2u

Q: Prove using the IVT. tan-1x = cos-1x has a solution.

A: Given :                      tan-1 x = cos-1 xSolve :                     tan-1 x = cos-1 x…

Q: 6) 1-cosx %3D 1+cosx (cotx - cscx)2

A:

Q: how that cos 1+cos 8 and sin 1-Cos 0 %3D %3D using de Moivre's Theorem.

A: It is required to show that cosθ2=1+cosθ2 and sinθ2=1-cosθ2 by using de Moivre's theorem. By de…

Q: Express the number 8√3-6i in the form R(cos(0) + i sin(0)) = Re, where R> 0 and - ≤ ≤T. NOTE: Round…

A:

Q: 15) tan- -1 Vz 17) cos -1 19) tan 1

A: topic - Inverse trigonometric ratios

Q: Show that the equation has exactly one real root. 2x + cos(x) = 0 %3D

A: Our Aim is to show that the equation 2x+cos (x)=0 has exactly onereal root.

Q: 15. Restate r= 5 cos 0 in rectangular form.

A:

Q: True or False sin ( 20) has two equivalent forms: 2 sin 0 cos 0 and sin² 0 – cos 0

A: Given statement is, sin2θ has two equivalent forms: 2sinθcosθ and sin2θ-cos2θ.   The objective is to…

Q: 7. Determine all the solutions to the equation in the interval [0, 27): sin 20 cos0 – cos 20 sin0 +1…

A: As we know that Sinx-y=SinxCosy-CosxSinyThe genaral solution of Sinz=-1  then z=Sin-1-1=nπ±π2

Q: Prove 3n - T, 2 sin? x – sinx cosx – 2 cos? x=0 in has five root's Hint. Intermediate value theorem

A: Corollary of Intermediate value theorem :- If a continuous function has values of opposite sign…

Q: 2) Verify that the equation is an Identity tan 0 %3D sin 0 sec 0 %3D %3D

A: We know that secx is the inverse of cosx and tanx=sinxcosx the objective is to prove the…

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

A:

Q: Q4:B/Simplify [cos 20-i sin20][cos 30+ i sin301² [cos 40+ i sin40 1³[cos 20-i sin2015 using De…

A: The given expression,      cos 2θ-isin 2θ8cos 3θ+isin 3θ2cos 4θ+isin 4θ3cos 2θ-isin 2θ5 De Moivre's…

Q: tan 30 + 2S in Go +Cos 30 -tan 60 4.

A:

Q: Cos2x dx (1-sin2x)4

A:

Q: Q4:B/Simplify [cos 20-i sin20][cos 30+ i sin3012 [cos 40+ i sin40]³[cos 20-i sin2015 using De…

A:

Q: 3. Express into standard form: = = 8[cos (-5) + + sin(-5)] Z i 3 3

A: Solution

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: VERIFY THE IDENTITIES

A: To verify

Q: Suppose that sin(θ)=2/6. What sec(θ)=______.

A: As we know that; The trigonometric ratios;…

Q: Why is V /5+ 5 tan² 0 = v5 sec² 0? Because Vtan 0 = sec 0 Because 1+ tan² 0 = sec² 0. • Because sec?…

A:

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

A:

Q: 2 Convert r = to rectangular form. 7 sin 0 COS

A:

Q: { 0, 1, sin’t, cos t, cos 2t } COS a cubcnnco? Juctifu vour

A: This is a question of linear algebra and vector space.

Q: Show that sin x – cos x< V2 V2 -

A: Take RHS first and work on that:

Q: Recall that sin2 0 means (sin 0)². find sin2 0. If sin 0 = sin< 0 =

A:

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: Show that the equation has exactly one real root. 8x + cos(x) = 0 %3D

A:

Q: Prove that; (a) cos4θ- sin4θ = cos 2θ  (b) Sin (π/4 + A) + Sin (π/4 - A) ≡ √2 cos A

A:

Q: Prove using trig identities sin 20° =1 V3 cos 20° – 2 sin 40°

A:

Q: Show that 4 sin x cos 2x + 3 = 8 cos %3D x.

A: We will use the formula of cos 2x and other formulas of trigonometry to prove left hand side is…

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