tan (x) -cot(x) tan(x) +cot ( x tan(x)+cot(x) +2cos (x)

Q: cos( - x) = O sin( - x) O cos( + x) cos( - x) sin( + x)

A: The given expression is: cos π3-x Note that: cos θ=sin π2-θ

Q: sin-1 3x - sin 3x lim x-0 tan-1 3x – tan 3x

A:

Q: .f (x) = cos(-x) .f(x) = sin(8x) .f (x) = 2 sin(-5x) a) f'(x) = 2 sec(2x – 1) tan(2x – 1) %3D - b)…

A: Since you have asked multiple question, we will solve the first 3 question for you as per our guide…

Q: VERIFY THE IDENTITIES

A:

Q: (sin x - cos x )² + 2cos x sin x

A: To simplify trigonometric expression

Q: limx0 cos x COS X 0-X. limr-o tan x limx-0 cot x

A: Definition and methods help to find the required limit of the given function. A value is said to be…

Q: sin'x+ cos x sinx 3 ,2. tan x sec x = 2 cos"x

A: use simple trigonometric relations to prove it.

Q: cosx sin'x = 3.. 3. cos°x sin°x= 5. = (sin°x- sin°x)cosx

A:

Q: sin x 1+ cosx 1+ cosx sin x 2cscx 2secx 01

A:

Q: Find the limit.

A:

Q: sin x-cos x sin x cos x 1. tan x csc x-secx cot x II

A: Hi,  As per bartleby rules, we are supposed to do only one question at a time.  Kindly repost the…

Q: sin 5x + sin 3x 2 cOS X 4 sin x cos 4 sin x cos x 3 X COS -

A:

Q: tan(sin(x)) tanx-sinx 4- lim x-0 5-lim x-0 sinx

A:

Q: sen x = 0,5 cSC X =. V3 cot x = tan x = cos x = -3 X = sec x = tan x = - /8 cot x = -5 cos x = sec x…

A:

Q: Use identities to simplify each expression.

A: cosxsin2x+cos3xsecx=cosxsin2xsecx+cos3xsecx=cos2xsin2x+cos4x…

Q: sec2 x + (sec x) (tan x) 1-sin x

A: Consider the identity  sec2x+secxtanx=11−sinx

Q: sin x- cos x sin xcosx- cos x .2 CoS

A: To simplify

Q: sin 2 x + sin x + cos 2 x - 1 = _______ tan x cot x sin x cos x

A: We can solve it as below.

Q: sin x 1+ cosx 1+ cosx + sin x 2cscx 2secx 01

A:

Q: (sin x + cos x) sin'x- cosx sin'x- cos'x cos-r COS X (sin x – cos x)2

A:

Q: tan(2 x) lim x→0 tan(x)

A: According to L'hopital's rule: If a limit has the indeterminate form of 00 or ∞∞ then differentiate…

Q: sin x COsx Prove 2tanx secx - - cosx 1+ sin x

A: We use the identity sin2x + cos2x=1

Q: (tan(x)/(1+sec(x)))-(tan(x)/(1-sec(x)))

A: Given:

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: sin² (x) x…0 COSX-1 7) lim cotx + CSCx X-T 5) lim cosx+1 6) lim X-7 sinx 8) lim(--)

A:

Q: Verify the following identity:

A: We have to prove the following trigonometric identity: sin4x2-cos4x2sin4x2cos4x2=-16cos xsin4 x

Q: lim x->0+ (sinx)^(tanx)

A: The given limit,limx→0+(sin x)tan x

Q: V1+ cos x + v1- cos x X =-+-,0<x<. 4 2 an 1+ cos x - V1- cos x - cOS X VI

A:

Q: Evaluate the limit.

A: To evaluatelimx→0sin5xsin2xsin3xsin5x

Q: 2 sec² x – 2 tan² x = sin 2x sec x b) sin (- x) cot ( + x) = – sin x a) CSC X

A: We will use  secx=1cosx,tanx=sinxcosx and  sin(π2-x)=cosx,cot(π2+x)=-tanx

Q: sin x 1+ cosx 1+ cosx sin x 2cscx 2secx 1

A:

Q: Find the limit

A:

Q: sin 2x + sin x + cos 2x - 1 = _______ cos x cot x tan x sin x

A: Solution ) sin2x + sin x + cos2 x - 1  = sin2 x + cos2 x + sin x - 1 We know that  [ sin2 x + cos2 x…

Q: sin(-x)+ cos(-x) = − sin x + cos x

A:

Q: lim sin (2 – 2) cot² (x² – x – 2)

A: We have to find

Q: tan(x) - cot(x) = sec(x)(2 sin(x) – csc(x)) %3D tan(x) – cot(x) sin(x) cos(x) %3D cos(x) sin(x)…

A: We can use the trigonometric identities, sin2x=1-cos2x,  cos2x=1-sin2x tan x=sin xcos x, cot x=cos…

Q: (Sin X-cos X)^2=1-sin 2x

A: Formulae to note: (a-b)2=a2+b2-2ab. 2 sin x cos x=sin2x. Sin2x+Cos2x=1.

Q: sin (-11x) lim x→0 _tan(9x) (x2-х)sin(x-1) lim х2-2х+1 X→1 tan x-sin x lim x3

A: The following properties will be used to solve the limits: a) limx→0sinxx=1 b)…

Q: Arcsinx-sinx 1. lim x→0 (1-cos2x)sin2x 2-2cosx-xln(1+x) 2. lim x→0 x sin² x

A: 1)

Q: sin (x) + cos³(x) = 1 - sin(x) cos(x) sin(x) + cos(x) sin (x) + cos°(x) - (sin(x) + cos(x)) (…

A:

Q: 2 sin x tan x - tan x = 1 - 2 sin x

A: Answer and explanation is given below

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: cos'x - tanx 5. prove it cot'x - sec'x sin'x 1+ sec x 6. sin'x sec x 1- cos x cosx 7. 1- sin x cos x…

A:

Q: coS x cotx cos x-sin x cotx -1 II

A:

Q: sin 3x-sin x 5. cos 3x+cosx tan x

A: Definition used -…

Q: sin(3x)-sin x - cot(2x)= cos(3x) - cos x

A:

Q: 2+ tan x - ) sec" x

A:

Q: (cot2 x + 1)(sec² x – 1)

A:

Q: sin x-cos x 1. tan x csc x-secx cot x sin x cos X 1 1 2 2. cscx-cotx cscx+cotx tan x 3. cos4x - sin4…

A: 1. sin x-cos xtan x csc x-sec x cot x=sin x cos x2. 1csc x-cot x-1csc x+cot x=2tan x3.…

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.