d 1 dr tan? (x)

Q: (A) Verify the identity (i) (1 + tan² x)(1 - sin2x) = 1 sec x - 1 %3D tan x (ii) tan x sec x + 1 1+…

A: We have to prove the identities.

Q: sec² 0 de tan² 0 – 1

A: Integrate the integral.

Q: establish each identity.

A: To prove this identity first we will use the result log(a)+log(b)=log(ab). Then the identity…

Q: tan"x jun's de - | tan"-x dx (n 1) n- 1 tan x sec" r sec x dx (n 1) n- 1

A:

Q: 1- sin x 1. = sec x-tan x COS X

A: Topic- trigonometry

Q: 2 n- tan x sec"- 9. Show that for n > 2, п-2 sec" x dx + n - sec" 1 x dx п — 1 | 4 Use this to find…

A: You need to use reduction formula to integrate the function, such that: You need to use integration…

Q: sin(2x) cos(2x) Prove sec(x) sin(x) cos(x)

A: Trigonometry

Q: sec 0 +1 – tan 0 , tan 0+ sec0 –-1 Prove : = 2 sec 0 sec 0 +1 + tan 0 tan 0 – sec0 +1

A:

Q: 2 tan x sin 2x 6.) 1+tan² x

A:

Q: 1- sin0 lim а) 1+ cos 20 2

A:

Q: tan (0) +1 1) sec(e) = sec(0) cos(@) +1 2) tan (0) cos(@) sec(@)-1

A: See the details solution in below

Q: 1+3x- cOs x 2.) lim tan x

A: In this question we need to find limit of the given function.

Q: tan(8x) x-0 sin(5x) is indeterminate of type Therefore lim We must use l'Hospital's Rule. The…

A: We are given to find the limit of limx→0 tan(8x)sin(5x); and we have to make use of L hospital rule…

Q: 1-cos(2x) sin²(3x) tan x-sin x Evaluate: a- limr-0* b- lim sin³x

A: (a) Given, Simply fie the above expression, On applying the limit, the solution is in 0/0 format.…

Q: 9. Establish the identity 1- sec 0 tan 0 2 cot 0 tan 0 1- sec 0

A:

Q: 1-cos 2x lim x2 sec x-tan x lim X→0 X→- 2 x- 2 x2 +sin 3x lim 2x+tan 2x . х-0

A: We are solving first question for you. If you want solution for any other question than please…

Q: lim cos2x-1/sinx x-> 0

A:

Q: sin 2x 4. tan x = %3D 1+cos 2x 19 5. tan %3D = CSC X - cot x

A:

Q: 1-cos(2x) - Evaluate: a- lim,-0 sin²(3x) tan x-sin x b- lim sin3x

A: According to L'hopitals rule,limx→af(x)g(x)= limx→af'(x)g'(x)iff(x)g(x)= 00or ∞∞. If there is any…

Q: 4. Verify the identity: (sec 0 + tan 0) (sec 0 – tan 0) = 1

A:

Q: 2 3 lim x2.tan=.sin- x) X-00

A:

Q: Prove: sec 0 + tan(-0) cot 0 - cos (0) = sec 0 tan 0

A:

Q: tan x -cot x sin x cos X %3D tan2x-cot2x 1-sin x %3D 1+ sin x 4. (sec x- tan x)² 3.

A: 3)tanx-cotxtan2x-cot2x=sinxcosxL.H.Stanx-cotxtan2x-cot2x=tanx-cotxtanx+cotxtanx-cotx=1tanx+cotx=1sin…

Q: 1 - sin x           1 - sin x ---------   -   ----------- = 4 secx tanx 1 - sin x           1 +…

A:

Q: sin(-æ) = - %3D V2 tan(x) = – %3D cos(x) csc(x) cot(x)

A:

Q: tan 7x i) lim x+0 sin 3x sin(x2 + 3x + 2) j) lim x+2 x + 2

A:

Q: How Prove that? 2tanX tan 2x 2 1- tan x

A:

Q: 8.1- secx - tan x tanx 1 secx

A: (1-secx)/tanx - tanx/(1-secx)

Q: 1-Cos 2x 1+ Cos 2x ix) tan x=

A: Prove :

Q: 2. 2) tan- 1 4) sin- 6) tan-1 V3 -1 01_ V3 10) sin -1 2. 12) tan-! 3.

A:

Q: √3 csc x − 2 = 0  tan 3x(tan x − 1)  sin2 x = 3 cos2 x

A:

Q: 7- I = [sec(2x) tan(2.x)dx cos(2x) 8- I = dx 4-sin (2x) csc (In(x)) 9. I: dx

A:

Q: sin (-8-2T) Sec co) arc tan (x) TT cos' (Gw) Sin' GW) dw CoS tant (2) sec (2)dz

A:

Q: 1-cos2.x sin 2.x : tanx

A: Given- 1-cos2xsin2x : tanx To Simplify- The above expression. Formula Used- cos2x=1-2sin2x and…

Q: I+ cosx+ cos 2x (ii)Show that sin x+ sin 2x tan 20 - tan 0 = tan 0 sec20 cotx (iii) (iv) (cose -…

A:

Q: * tan°(x) cos“(x) 1 tan7(x) 1 tan (x) O tan7(x),

A:

Q: 1+sin θ=(sec θ-tan θ)^2 +1

A: To evaluate theta.

Q: 1 sec x – tan x sin x = %3D secx

A: Consider, secx-tanx sinx=1cosx-sinxcosx·sinx=1cosx-sin2xcosx=1-sin2xcosx=cos2xcosx…

Q: (5) f(x) = cos (5 - 2x) (7) f(x): = cos (√x³ + 1) (9) f(x) = cot (x5) (6) f(x) = cos (4x7 + 3) (8)…

A: Note: As per company guidelines we solve only first three subparts when multiple parts question…

Q: solve using L'Hopital's Rule 7. Lim    1/(tan-1)2  -  1/x2    x->0

A: Given the limit as : limx→0 1tan-12-1x2 We need to find the limit by using L' Hopital's Rule. Let's…

Q: 4. (tanx)(1 - cot x) = tan x - 1

A: Given  (tanx)(1-cotx)=tanx-1 Let's verify the identity as shown below

Q: tanx(1+cot^(2)x)=(1)/(cosxsinx

A: To prove tanx1+cot2x=1cosxsinx consider the left hand side  tanx1+cot2x=1cosxsinx we know that…

Q: Find the limit

A:

Q: 1-cos(2x) limx→0 sin² (3x) tan x-sin x lim - Evaluate: а- b- x→0 sin³x

A:

Q: 1-cos(2x) tan x-sin x Q6- Evaluate: a- limx-0 b- lim x-0 sin (3x) sin³x

A:

Q: 2+ tan x - ) sec" x

A:

Q: Prove sin 2  x/2=  tan x - sin x / 2 tan  x

A: The given identity is sin2x2=tanx-sinx2tanx

Q: 1-cos 2X lim x→0 x2 sec x-tan x lim X→- X- 2 x2+sin 3x lim r20 2x+tan 2x

A:

Q: sec x-tanx lim X→- 2 2 х2+sin 3x lim х-0 2х+tan 2x

A: Let us consider limit of the function L=limx→af(x)g(x) On applying the limits of the  00 form then…

Q: 1- sin 0 Prove that = sec 0 - tan 0 1+ sin e

A: Square on both sides of the given relation We get