tan x sin 3x lim X-→ 3. sec cot 2x

Q: Verify (tan x + cot x)(cos x + sin x) = cscx + sec x sin* x – cos“ x = sin? x - cos? x

A: Given that prove tanx+cotxsinx+cosx=cscx+secx   And sin4x-cos4x=sin2x-cos2x

Q: secx tan.x 5) 1+ sec x

A: Use the method for substitution.

Q: Evaluate: lim 2 tan (r – 2) sin(x – 2)ª

A:

Q: TT+tan x 5. lim sin tan x-2 secx.

A:

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

A: Topic- trigonometry

Q: find the given limits

A: The given limits,

Q: The value of lim sin x- cos x 1s 2 sin x+3 cosx

A:

Q: If y = sin x, then y' = - cot x sin x - tan x sec x sec x -sin x - Cs X tan x cos X CSC X

A: Given function is y=sinx. Differentiating the given function with respect to x, we get…

Q: sin 3x cot 4x lim cot 5x

A:

Q: [tan (x)sec (x)dx cot (x)csc°(x)dx sin (x)cos (x)dx

A:

Q: sin (x) – cos²(x) Show that 1 F COS %3D CSC (x)

A:

Q: lim xS0  .  ...........tan 3x / sin 8x

A: limx→0tan3xsin8x

Q: 2. tan x csc x + cot x sin x = sec x + cos x

A: As you mentioned question no 2 solved

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: tan(5x) (1) lim 40 sin(3x) sin(6x) (2) lim x-0 4x3 – 5x

A: 1) limx_0tan(5x)/sin(3x) 2)limx-0sin(6x)/(4x3-5x).

Q: tan 2x 5. lim→0 sin 5¤

A:

Q: (tan'x de 3 1. [cse* xdx 4 2. csc"xdx 3. |tan 3x sec 3xdx

A:

Q: tan x csc x(1+ sec x) ove 1- cos x %3D

A: you need to know these formulae before solving the question:

Q: lim »0 sin(2t) tan(7t) is t2

A: Here we find the value limt→0sin(2t) tan(7t)t2

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

A:

Q: Verify the identity.   1 + sin x 1 − sin x  −  1 − sin x 1 + sin x  = 4 sec x tan x

A: The given identity is,

Q: Evaluate the limit.

A:

Q: lim (sin x)tanx TT 2

A: We will solve the problem

Q: sin x cot x (1 – COs x Prove - (sec x+1)

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Find the limits in Exercise

A: The limit of a function(expression ) is a value of that function (expression ) approaches as the…

Q: 1 sec @ — tanө %3D sece + tan0

A: rationalizing LHS and using trigonometry formula's to get RHS

Q: tan x - X 1. lim sinx 5 A. 2 В. 2 С. О D. undefined

A:

Q: In(|tan(x) sin(x)|) = 2 In(|sin(x)]) + In(|sec(x)])

A:

Q: cot(sec¬1(x))

A:

Q: 5 sec(x) − 5 cos(x) = 5 sin(x) tan(x)

A:

Q: | tan° xsec* xdx 6 2. Use 1 + tan² x = sec? x to evaluate

A: Solution:

Q: (tan x\secx) _ 1 1 - sin' x sin x L.S.

A:

Q: 1 sec x – tan x sin x = %3D secx

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

Q: = If f(x) = f'(x) = ƒ'(5) = 4 tan x, then - sin(x)-4 sec² (x) Cos x

A:

Q: | (tan x)¬3/2 sec² x dx

A:

Q: secx-tan x cos x 10. secx+tan x 1+sin x

A:

Q: tan? x – cot2x = sec2 x – csc? x - tanx-sinx = 1- cosx tanx

A: To prove :- 5.tan2(x) - cot2(x) = sec2(x) -csc2(x)  6. (tan(x) -sin(x))/tan(x) =1-cos(x)

Q: Lim sec(2x). tan(3X)

A: We have to find the limit.

Q: T+tan x 4. lim sin X→0 tan x-2 sec x,

A:

Q: 4 cot x)sec& ) .

A: cotx = cosxsinx. secx = 1cosx csc x =1sinx

Q: 6) Verify tan x + cot x = sin(2x)

A: Simplification

Q: ind lim tant sec2t

A:

Q: 2. Verify: sin x+tan x %3D sin?x sec x csc x+cotx Sink+tanx

A: We have to prove the identity

Q: sinx + sin 2 Evaluate | cosx A. -In cos x|– x+ C В. In'secx-x+ C C. -In|sec x|+ x+C D. In sec x|+x+C

A:

Q: Prove tan x + cot x = sec x csc x.

A: we have to prove tan x + cot x = sec x csc x.

Q: (sec(x) + 1)/(tan x) = (sin x)/(1 - cos x)

A:

Q: sin 7x cot 4x lim x cot 3x

A:

Q: Evaluate: lim (1+sin 4x)cot ¤ x→0+

A: Topic:- limit calculus

Q: prove  cosx( 1- tan x)= cos x- sin x

A: