OO Verifying a Trigonometric Identity In Exercises 37–42, verify the identity. 37. sin'/2 x cos x – sin5/2 x cos x = cos³ x/sin x 38. sec“ x(sec x tan x) – sec* x(sec x tan x) = sec³ x tan³x 39. (1 + sin y)[1 + sin(-y)] = cos² y tan x + tan y 40. cot x + cot y 1 - tan x tan y cot x cot y – 1 1 + sin 0 1 – sin 0 1 + sin 0 |cos 0| 41. cos x - cos y 42. sin x + sin y sin x - sin y = 0 cos x + cos y

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: tan? x sec² x + secx Prove -cos x

A:

Q: prove identy show steps sinx/1-cosx  - 1/sinx = cotx

A: To prove the given identity, we are taking left hand side,

Q: An inverse tangent identity a. Use derivatives to show that tan¬x + tan(1/x) is constant, for x > 0…

A: To show that tan-1x + tan-1(1/x) is constant, differentiate tan-1x with respect to x. Differentiate…

Q: tan x csc² x-tan x sin x tan +cos x cos² cos? x csc x Prove Show all work to receive credit

A: Apply the basic trigonometric formulas and simplify the terms.

Q: secx-tan x cos x %3D 1+sin x secx+tanx

A: consider the left hand side of the equation sec x -tan xsec x +tan x sec x -tan xsec x +tan x=1cos x…

Q: cosx+sinx=cos(2x)  Prove that tanx=-1

A:

Q: 2 Using the relation 2 (1 cosx) x, V x € (0, - · 4)

A: A relation is given by, 21-cosx < x2, where x≠0. The objective is to use the given relation to…

Q: Prove the identity. sinx 1+ cos.x 2 cscx 1+ cos.x sinx

A: Given, The identity  sinx1+cosx+1+cosxsinx=2cscx We have to prove the identity.

Q: (csc x- cot x)2 = 1- cos x %3D 1+ cos x

A: To prove: (csc⁡x−cot⁡x)2=1−cos⁡x1+cos⁡x We know that csx = 1sinx, cotx=cosxsinx

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

A: use simple trigonometric relations to prove it.

Q: tan x - cot x Cos 2x Cot X t tanX

A: Given: tanx-cotxcotx+tanx=-cos2x

Q: verify the identity    2cot2x= cotx- tanx

A: To verify: 2cot2x=cotx-tanx Solution: We know that cotθ=1tanθ And we have formula,…

Q: sin (In (x))x

A:

Q: Prove the identity. sin'x cos'x = (cosx-cos x) sinx 3. cos x- cos x) sinx

A:

Q: sinx-cos x 1. tan x cscx-secx cot x sin x coS X %3D

A:

Q: cos(-x)+sin(x=x) Q4 prove that sinx 2

A:

Q: Verify identity sec x - sec x sin2 x = cos x.

A: Given ,           sec(x) - sec (x)sin2(x) = cos (x).

Q: inx-cosx -= sin x cos x сх-sec x сot х 1 cotx cscx+cotx tanx < – sin*x = 1 – 2 sin² x cot x sin x…

A: According to our guidelines we can answer only three subparts, or first question and rest can be…

Q: 1- sin2x/1+cos x=cos x. Verify the identity

A: The given identity:

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

A: We use the identity sin2x + cos2x=1

Q: 24. Prove the identity sec(x) (sin(x) + cos(x)) sec(x) + 2 sin(x)

A:

Q: tan x csc x-tan x Prove Cos“ x csc x sin x tan +cos x

A: tanx csc2x-tanxsinx tanx+cosx=cos2x cscx

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

A:

Q: 1-cosx sinx B: Prove sinx 1+cosx

A: Consider,  LHS=1-cosxsinx       =1-cosxsinx×1+cosx1+cosx       ....(muliply and divide by 1+cosx)…

Q: sin(x+y) Verify that (sec x cos y + sin y csc x) %3D sin(2x)

A: Prove that sin(x+y) /sin2x?

Q: Verify the identity. 1 + sin(x) 1 - sin(x) 1- sin(x) 1 + sin(x) 4 tan(x) sec(x)

A:

Q: 1-cosx sinx B: Prove sinx 1+cosx 1-cosx C: Prove tan? 2 2 1+cosx

A: As per our guidelines we are supposed to answer only one or two question. Kindly repost other…

Q: sin5x + sinx Verify the identity. = tan 3x cos 5x + cos.x

A: To verify the identity. sin5x + sinxcos5x + cosx = tan3x

Q: Verify the folowing equation is an identity with work shown…

A: We need to check whether the given equation is an identity or not.

Q: sec x+1 tanx tan x secx-1

A: We have to proof

Q: 2. Verify: sin x+tan x %3D sin?x sec x cSc x+cotx

A:

Q: sinx 0 cosx –sinx cosx is non singular for all values of x. 1 lect one:

A:

Q: Smx sınxtanx+ a) Explain the method for proving tanx cosx is an identity.

A: The method to prove the given identity is to transform the the any of the sides equal to the other…

Q: sin x Verify: cot x + = csc x 1+cos x

A:

Q: Verify the identity. 2 tan(x) 1 + tan2(x) 2 tan(x) sec2(x) sin(2x) 2 tan(x) 1 + tan?(x) 2 sin(x) .…

A: The prove that  (2tanx)/(1+ tan2x) = sin2x

Q: rove the identity. sin(3x)/sin(x)cos(x)=4cos(x)-sec(x)

A:

Q: COs x + sinx COS x - Sln x - sin = 2 tan 2x %3D Cos x- sin x COS x + sin x

A:

Q: Prove the identity 1÷(1-sinx) =sec^2 x +tanx secx

A: 1(1-sinx)=sec2x+tanxsecx

Q: sin 2x/1-cos 2x =cot x. verify the identity

A: Consider the given equation.

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: sin 2x+cos2x+1 1- Prove cot x %3D sin 2x-cos 2x+1

A:

Q: complete identity cosx + sin x/ cos x - sinx - cosx/sinx = ?

A: simplyfy

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

A: Definition used -…

Q: cosx Prove the identity: tanx+ sec x 1+ sin.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- sin(-x) 11. cos x+ cos(-x)sin = sec x

A: Dear student as per our rule in one session we can only solve one question. Please post the other…

Q: Prove the identity. tan(x - ) - sin(x -) -cot(x) %3D tan(x -) - sin(x) cos - cos(x) sin() + sin(x)…

A: We have to solve

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.…

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.