Verify the identity. 2 tan(x) 1 + tan?(x) sin(2x)

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: sin? x 1- 1-cos x =-COS X

A: Here we have to use the basic trigonometric identity sin2θ+cos2θ =1 and we know that  a2-b2=…

Q: tan? x 1+ 1+ sec x

A:

Q: 27. What is the simplest form of sin 2 tan'x A) 1+x B) 21+x? 2x C) 1+x 2x D) |1+x?

A:

Q: n of the coefficient/s when we evaluate (sec(x) - tan(x))²dx

A:

Q: 3 sin° x -dx Evaluate ' cos° x

A:

Q: (÷++) + co« (5 - ). cos 3 x ) is equivalent to O cos 2x cos x O sin x cos x

A:

Q: Verify the identity:

A: Our Aim is to verify the identity given below:-sin 3π2-x=-cos (x)  -(i)

Q: 7. What is the exact value of tan (-105°)? O -2 – V3 O 2 - V3 O 2+ v3 O -2+ V3

A:

Q: 3 sin z – sin a cos² x = sin³ r

A: NOTE: Refresh your page if you can't see any equations. . here left-hand side is

Q: CianXtl) 2 tan x 8. Prove the identity: sin 2x = 1+ tan x L.S. es

A:

Q: 1. tan xsin x + cos x

A:

Q: (a) Find S(tan x)dx (b) Evaluate i sin 3x cos 3x dx d (c) Find (2x sin 2x + cos 2x) and hence…

A: a) ∫tan2πx dxb) ∫π9π6sin3x cos3x dxc) ddx2xsin2x+cos2x and ∫0π4x cos2xdx

Q: Right, or wrong? Give a brief reason why. sin (x²) x cos (x²) – sin (x²) dx х x²

A: We will try to differentiate the right side and check if we get the expression inside the…

Q: 4 sin? r d) lim a-0 3x tanx

A: see below the answerHere we use the L'Hospital Rule islimx→af(x)g(x) is of the form 00 then…

Q: tan? x (1 + sin² x) dx cos? x 4 cos (a) x2 dx x3 sin3 (-) | V4 - V4-x dx

A: We have to solve the integral.

Q: 1 Evaluate: sin'x cos x

A:

Q: sin 0 If 1+cos 0 x2 x2, then tan 2 - a) b) 4 c) x2 + 1 d) x2 |3| 2.

A: Given,  sin θ1+cos θ=x2 To determine tanθ2

Q: Evaluate sin? 3x lim X0 1- cos 2x

A: The objective is to evaluate limx→0sin23x1-cos2x Since, limx→0sin23x1-cos2x is 00 form.

Q: Using (11) and (12): 1 dx 1+ cos x tan +c

A:

Q: A. Bernoulli's Egquation 2. (3 tan X - 2 cos y) sec?xdx + tan x sin ydy - 0

A: Explanation The equation is in the form dydx+P(x)y=Q(x)yn is called the Bernoulli's equation Now we…

Q: | a 0.24) tan(sin-1x) = b) c) =x d) 1 - x2 3

A:

Q: Prove the following 2 tan 0 a sin 20 1+ tan? 0 2cos' x-cos x b cot xe sin x - 2 sin' x

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Q: Complete the identity. sin 2x- tan x = ? O A. tan x cos X O B. - tanx cos 2x O C. tan x cos 2x O D.…

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Q: 1. sin x csc x 5. cos² x (tan? x + 1)

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Q: 4 sin(A) – cos(A) | If tan(A) = , then %3D %3D 4 sin(A) + cos(A)

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Q: I = cos? x sin x In(cos x)

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Q: Prove the identity: sin (x-y) tanx- tany cosx cosy

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Q: 7. Prove the following identities. sin x 1 + cosx 1- cos x a. 1-cos x b. 1 + cos x tan? %3D sin x II

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Q: n(en sin-lx ) dx cos(sin -lx) +C Vī-x? 1–x2 A) True B False

A:

Q: Let x= 2 tan theta, 0 less than or equal to theta < pi/2  simplify the expression  1/x^2…

A:

Q: NIX 2. sin? x+(1-cosx) 2 tan %3D (sin x)(1+cos x)

A: We can verify the statement as below

Q: 13. Write sin(tan-)) ; x > 0, as an algebraic expression of r. 49 + x² iv) 7 ii) 49 + x² iii) 49 +…

A:

Q: 4. f(x) if f(x) - In(sin?x cos?x) a. 4 tan 2x b. 2 tan 2x c. 4 cot 2x d. -4 cot 2x

A:

Q: Using the identity, sinh y cosh y + i cos? x + sinh? y sin x cos x tan(x + iy) : cos² x + sinh² Y…

A: Given that, tanx+iy=sinxcoscos2x+sinh2y+isinhycoshycos2x+sinh2y Now,…

Q: 2 sin? x 7. lim x→0 5x(1+cos x)

A:

Q: Complete the identity. sin x COS X =? sin x COS X O A. sec XCSC X O B. sin xtan x O C. - 2tan x 2.…

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Q: The root of sin x - (1 /3) x = 0 close to x = 2.2. %3D

A: We have to find the root of sinx-13x=0 close to x = 2.2.

Q: 2 sec? r 1 1 Prove the identity: 1-sin x + 1+sin x

A: This is trignomertric question

Q: Evaluate and show your work a. sin (π - x) + cos (3π/2 - x) b. sec3π/4csc5π/4 + tan4π/3cot11π/6…

A: To Evaluate: a. sin (π - x) + cos (3π/2 - x) b. sec3π/4csc5π/4 + tan4π/3cot11π/6 c. Tan-1(-√3)

Q: CoS X Which of these is an efficient first step in proving the identity 1+ sin x 1- sin x :? cos X

A: To prove cos x1+sin x=1-sin xcos x

Q: p(x) = sin cos x Select the correct response: tan x O 1 O sin? x – cos² x 2 COS“ x -

A: Given that

Q: 3+(e*+3) sin x %3D tan(x³)-x

A: y=6x3+(ex+3)sinxtan(x3)-x

Q: • tan°(x) Xp- cos“(x) 1 1 tan9

A:

Q: 3) f(x) = cos (tan³(sin (x³))) %3D

A: Given, f(x)=cos5tan3sin2x5 now we apply chain rule to derivate ddxf(x)=ddxcos5tan3sin2x5

Q: cos 2x+sin? x 1.4 a) Prove the identity: =1- sin x. 1+ sin x

A:

Q: 5(cos²æ – 1) sin x cos x sin x - ||

A: Using trigonometric formula, given trigonometric function is simplified.

Q: sin?(x) + 5 cos(x) + 13

A: Given: Sin2x +5cosx+13