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

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

A: Establish the identity

Q: Cos x = Cos" x 1-

A: In this question we have to prove cosx=cos-1x.

Q: 1 - cos 2x if y = prove 1 + cos x y' = 2tanx.sec²x

A:

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

A:

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: - 1, z = cos-

A:

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

A:

Q: 1- Determine. 4. Cos 'x sinX dx

A: Given:                     ∫cos4(x) sin(x) dx     Solution:                    Integrating the given…

Q: s nip

A: Given z=tanα2

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

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

Q: 2) VERIFY THE IDENTITY sin +0 =-cos 0. 2.

A: We need to verify the identity.

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

A:

Q: 9. [cos° { xsin’ } xdx

A: The objective of the question is evaluate the indefinite integral.

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

A:

Q: 4. Verify the identity sin(z+y) %3D COB E COS y tan z+ tan y

A: “Since you have posted multiple questions, we will solve first question for you. To get remaining…

Q: 12 "2 If Y= \n(Sinae), Prove y =y=- ノ

A: Here, the given function is: y=ln(sin x) So, y'=1sin x(cos x)=tanxy''=ddx(y')=ddx(tan x)=sec2x

Q: 3. Prove that the identity is true. sin*t- cost = tan²t-1 cos't

A:

Q: 3. Show that cos 30 = cos 0 – 3 cos 0. [Hint: Apply De Moivre's Theorem.] |

A: Given: verify that cos3θ=cos3θ-3cosθ according to given hint theorem cosx+isinxn=cosnx+isinnx

Q: * Prove: sin x = cos COS 2- 2cos x

A:

Q: 3. If cos x = -, find sin(2x) given sin x < 0. -3 O O

A:

Q: 1. If z = sin2+In^, find the value of x- +y X

A:

Q: E prove that - Cotx + C %3D 2 |- Cos?x +Sinx

A:

Q: |12 sin(4x) cot(cos(4x)) dx

A:

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

A:

Q: Use Simpson's rule with n = 4 to approximate 3 cos(x)

A:

Q: 21 Prove the identity.cos x (1 ²x) 2 2. - sin sec X,

A: Consider the given identity cos2x1-sec2x=-sin2x.

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: Use Simpson's rule with n = 6 to approximate cos(x) rp-

A:

Q: 2) Verify. cot8 ese 6 %3D sin 6 tan 6

A: Use the following identities:

Q: 4. Prove that cos(sin¬1 x) = /1 – x².

A: cos(sin-1x)=1-x2⇒sin-1x=cos-1(1-x2)Let y=sin-1x                               (1) ⇒siny=x…

Q: Suppose, z=-i+1.7 then, Find e-iz e(cos 1.7 +i sin 1.7) e(cos 1.7 - i sin 1.7) (cos 1.7 - i sin 1.7)…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 9. Prove. cos x sin x 1 - csc x %3D sec x

A:

Q: y cos?£ 1-CUSE tanzz

A:

Q: 7. Evaluate Arc cos(j2).

A: It is principal value.

Q: 35. Use property IV of Appendix A to verify that 1 L'{arctan(a/s)} =sin at

A:

Q: (7) Find sin(5x) cos(4x) dx

A: Topic:- application of integration     Note:- as per our guideline if more than one question…

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

A:

Q: 12. Write an éxpression that gives all sölutions to the equation. COS X - SIn x 3= 2.

A:

Q: 4/ Prove that: " cos bx dx = (bsinbx +a cos bx]+c

A:

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

A:

Q: 23-Frove that. Cos3e - Cos'e- 3 Cos e Sin'e

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: e). Prove that Sin3A+sinA 25in2A -COSA

A:

Q: Show that sin²(x) cos(x) = sec(x) – cos(x)

A: We need to show the following. So,         Manipulating right side=secx-cosx=1-cos2xcosx=sin2xcosx

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

A: Solve the integration

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: Differentiate the following: 1. sinocose 2 csce -coto tan@sece 3 (cos 0-1)0

A: Topic:- derivatives  Note :- as per our guideline only first three subparts need to answered

Q: If sinx = siny = a and cosx = cosy = b,then cos(x-y) is

A:

Q: In sine sin -1x os (sin-!x) + C cos V1-x? 1-x² A) True В False

A: To check:  ∫sin(elnsin-1x)dx1-x2=-cos(sin-1x)+C is true or false.