Verify the identity algebraically. Use the table feature of a graphing utility to check your result 8 8 + = -16 csc(x) cot(x) cos(x) + 1 cos((x) – 1 8 8 - 8 + 8 cos(x) + 8 + cos(x) + 1 cos(x) 1 (cos(x) + 1)(cos(x) – 1) cos²(x) – 1 -sin?(x) cos(x) sin(x) -16 · sin(x) = -16 csc(x) cot(x)

Q: 2. Prove the identity: (cos x- sin x)2 + (cos x + sin x)2 = 2. %3D

A: To prove  that cosx-sinx2+cosx+sinx2=2

Q: Prove the identity. cos(x-y) / cosx cosy = 1+tanx tany

A: To Prove:cosx-ycosxcosy=1+tanxtany

Q: Prove the identity. Cos(x− 90°) − Cos( x + 90°) = 2 sin x

A: We will use the formulas: cos(A-B)=cosAcosB+sinAsinBcos(A+B)=cosAcosB-sinAsinB

Q: 2 cos2(0) - cos(O) - 1 = 0

A:

Q: Prove the identity. sec2 (x/2)= 2 sec x + 2/sec x + 2 + cos x

A: The given equation is,

Q: -t 2 lim 8 cos t ||

A: Given  The limit is limt→π2t2-π2t8cos t

Q: Q3) Use the addition formulas to derive the identity of (cos (x --): sin x ) %3D

A:

Q: Verify the identity. cos(+ x) + cos(-x) = = COS X X- cos(+ x) + cos(-x) = 2 cos ( 2 COS ( + + x + =…

A:

Q: Verify the identity.

A: 2cos⁻¹x = cos⁻¹(2x²-1) , 0 ≤ x ≤ 1 RHS = cos-1(2x2 - 1)Let cos-1(2x2 - 1) = AcosA = (2x² - 1)cosA +…

Q: Prove the identity. cos(3x) − cos^3 x = − cos x sin^2 x − sin x sin(2x)

A:

Q: Prove that there exists a value of x so that COs x cos-1 COS

A:

Q: 1. Solue cos ( x - 2) = 7

A:

Q: Derive/Prove: sin 2x = 2sin xcos x Useful Formula: cos 2x = cos?x-sin? x a. = 2 cos x-1 =1-2sin x…

A:

Q: Develop a formula for cos(3θ) as a third-degree polynomial in the variable cos θ.

A:

Q: Prove the identity. cos (x-y) 1+ tanx tany cosx cosy

A: cos(A-B) = cos(A) Cos(B) +sin(A) sin(B)

Q: Locate and identify the absolute extreme values of cos (ln x) on [1/ 2, 2].

A:

Q: Prove the identity  Cos x/1+sin x + Cos x/ 1-sinx = 2sec x

A:

Q: sin(2x) 1 Prove the following identity: cos(2x) - 1 - tan(x) sin(2x) %3D cos(2z) - 1

A:

Q: Prove the identity. 1- cos X = (csc x- cot x)² %3D 1+ cos X

A: Prove that , 1-cosx1+cosx=cscx-cotx2

Q: Prove the identity. cos(x + y) + cos(x – y) = 2 cos(x) cos(y)

A: It is given that,

Q: 1-cos 5x cOS lim 6x

A:

Q: 16. Establish the identity: os 0)² + (sin 0- cos 0)2 = 2 %3D

A: We need to establish the identity  (sinθ+cosθ)2+(sinθ-cosθ)2=2

Q: Q1 : limx¬1 x(1 – cos-)

A: To find the limit

Q: Describe what is wrong with the simplification shown. cos x - cos x sin^2 x = cos x - cos x (1 +…

A: Just simplyfing the above question we have

Q: cos    1 2 arccos x

A:

Q: 2 csc x 1+ cos x 1- cos x

A:

Q: find cos x if cos 2x=1/9

A: Consider the equation

Q: Simplify (cos x- sin x)(cos x+ sin x). sin x cos x O 2 cos x-1 2 cos x+1

A: Given: cosx-sinxcosx+sinx

Q: Verify the identity. cos (x+ n) = - c COSX

A: It can be varified using the formula for cos(A+B)

Q: cosxtanx - cos x= 0 + O 0+n,+ 2nx 5я O O+*5, + 2nx 5я

A:

Q: Q1: lim,-1 x(1 – cos-)

A: The objective is to find the value for limx→1x1-cos1x Since the given function is continuous…

Q: VERIFY THE IDENTITIES

A: To verify

Q: verify that el0 + e-i0 COS %3D

A:

Q: Prove the identity  cos(x+y)/cos x * cos y = 1- tan x * tan y

A:

Q: Prove cos* x – sin* x =1–2sin² x

A:

Q: 1 cos²(x) 2

A: The given question as belonging to the calculus in which we have to find the given integral so now…

Q: Evaluate the limit of x —> negative infinity. Cos (2x) / x+25

A: To find limx→ -∞ cos2xx+25

Q: x + 2 cos x 20. у -

A: If y = u/v, y' = (v*u' - u*v')/v^2.  d(cos x)/dx = -sinx d(x+2) = d(x) + d(2) = 1.

Q: COS X 2- COS X

A: Given integration is: ∫cosx2-cosxdx To find the value of integration.

Q: (a). Find a common denominator for COSX |- COSX and 1- COS x COS x –COS X COSX = cosx-coseX COS X…

A: a To find a common denominator for 1cos x and cos x1-cos x.b To expand cos x+tan x2 and to simplify.

Q: 1. Evaluate 2. Evaluate sin(20) 30 x-2x cos x sin x limo lim, 0

A: Given is  limθ→0sin(2θ)3θ. L'Hospital rule: limx→af(x)g(x)=limx→af'(x)g'(x) NOTE: According to the…

Q: 4. Verify the identity: 1 cos(x)+1 1 + cos(x)-1 -2 csc(x) cot(x)

A:

Q: Show and briefly explain your steps to find the exact con [tan-+ sin (-) „y the 1 1 5 + sin value of…

A: Given that: costan-112+sin-1-213

Q: |2x cos (x² -5) х cos

A: To find value of ∫2xcosx2-5dx Solution: Let substitute t=x2-5 Differentiating both sides with…

Q: 2. lim /1 + cos(п сос х).

A:

Q: Verify the identity. cos (x+n) = - COSX

A: By using trigonometric formula, we verify the given identity

Q: Let cos x = 3/4 with x   cos  2 x

A: cos2x=2cos2x-1

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.