A. PROVE THE FOLLOWING IDENTITIES: 3. tan*x + tan²x = sec*x – sec'x tanx+secr-1 1+sinx tanx-secr1 cosx

Q: 8. Evaluate the integral. sin x xp. 4+ cos x

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Q: Find the periodic function f(x) = sinx + tan-+ sin- X + 23 + sin 2n+1 + tan ... 2n

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Q: - i) By using L'Hopital Rule, find sinx lim x-0 e3x 1 ii) Given that a = sin V3 2, find, csca -1

A: In L Hopital's rule take the derivative of numerator and denominator separately and than put the…

Q: Express tan a using x. 3

A: We have the right-angled triangle. Let us label the small triangle ABC, the big triangle ABD and the…

Q: Integrate the following. - sec²x 3. ( sec?x tanx

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Q: tan 0 de equals to : 1+sece In |1+tane|+c In |1+sece|+c O (tane)^2/2+c -In |1+cose|+c

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Q: 8. Show that sin a (1+ tan a) + cos a (1 + cot a) = sec a + csc a.

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Q: Q4: Prove that: (1- sin x)(1 + cscx) = cos x* cot x %3D

A: To Prove1−sinx1+cscx=cosx×cotx

Q: 6. By using u = tan 0, evaluate | tan 0 sec*e de .

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Q: 4. Verify the identity sin(z+y) %3D COB E COS y tan z+ tan y

A: “Since you have posted multiple questions, we will solve first question for you. To get remaining…

Q: 3. Prove that the identity is true. sin*t- cost = tan²t-1 cos't

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Q: EX-15- Prove that : a) Sec-'x= Cos- ! b) Sin-' (-x)=-Sin-'x

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Q: 8-Prove the following identities. ( [Tan2x/ (secx -1)] -1= secx Cos x+[sin2x/(1+cosx)] = 1

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Q: -sin (In x?)ecos² (In x) dx 100x2-x2e2 cos (In x)

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Q: Verify the identity sec-1 x = cos-1(1/x), for x ≠ 0.

A: According to the question, we have to verify the identity sec-1x=cos-11x. As the above function is…

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

A: We need to prove the following identity cosx+ycosx cosy = 1-tanx tany

Q: Prove using the IVT. tan-1x = cos-1x has a solution.

A: Given :                      tan-1 x = cos-1 xSolve :                     tan-1 x = cos-1 x…

Q: DO NOT include spaces in between characters. * = <x<0. Given that tan 2r =-2, solve for tan x. 4 Let…

A: The given data is: tan2x=-2, -π4&lt;x&lt;0 Solve for tanx.

Q: Show that x² + 1 cos{arctan[sin(arccot x)]} = V x² + 2

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Q: USE THE SECANT METHOD IN FINDING ROOT/S STARTING AT XI-1=-0.1 AND XI=0. (NOTE: UTILIZE UP TO 4…

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Q: (2k + 1). True or False tan 0. cos 0 = sin 0 for any 0 + %3D

A: Given :            tan θ . cos θ = sin θ for any θ ≠ (2k + 1)π2.  To state true or fase.

Q: E prove that = - Cotx + C %3D 1- Cosx +Sin'x

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Q: 1. What is S tan x dx?

A: log|sec x|+c .

Q: 46 a Show that cos x+ =-sinx. = -sinx. d" (cosx) = cosx + drn b Prove that

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Q: Find the limit of tan(4x)/sin(6x) as x approaches zero.

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Q: 3. Prove the identity : sin(x- y) tanx - tany cosxcosy

A: The given identity is, tanx-tany=sinx-ycosxcosy The identity will be true if the left-hand term will…

Q: 1. Differentiate the following with respect to the variable given. 1 cosx 2 sin x tan 2. Given the…

A: We can solve the given problem as follows:

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

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Q: x is in the interval [0, 2t) * sin2x - cos2x = 0 COS

A: Given: sin2x-cos2x=0; x∈[0,2π) We know that cos2A-sin2A=cos2A…

Q: (a) Show that tan x = dx sec?x using quotient rule.

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Q: 9. Prove. cos x sin x 1 - csc x %3D sec x

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Q: Q1 : limx¬1 x(1 – cos-)

A: To find the limit

Q: HW/ Prove that: (1) 1-tanif x sechx

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Q: Verify the following identities. SHOW EVERY STEP!!! a. sin θ/1+sin θ = tan θ secθ - tan2 θ b. 2…

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Q: Evaluate: | sech[In cosx]tanx dx A -2 tan -1(e cosx) +C В -2 tan -1(cosx) +C 2 tan -(ecosx) + C (D 2…

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Q: Q4) Prove that 1- Cos +x) = sin x, 2- (sin x +cos x) sec x see' x

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Q: S cos3 x sin* x dx

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Q: 5. Verify the following trig identities: A. secx tan x sin x = cos x B. secy_tany =1 cos y cot y C.…

A: The given query is to prove the following trigonometric identitites: secx-tanxsinx=cosx…

Q: 1 tan 0+ 1 sin 0 sin (90° – 0) tan 0 -

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Q: 4. Use Walli's formula to evaluate 2 sin*x cos°xdx.

A: Given integral is as below:-                  ∫0π2 sin4xcos9xdx

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

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Q: 2. Prove the following identities: a) tanx + cotx = secxcscx cosx + 1+sinx cosx b) 1-sinx cosx

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Q: Show that tan(arccosx) for |x| s 1, x + 0.

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Q: USE THE SECANT METHOD IN FINDING ROOT/S STARTING AT XI-1=-0.1 AND XI=0. (NOTE: UTILIZE UP TO 4…

A: Given : fx= cos x +2 sin x +x2      xi-1=-0.1   and  xi= 0 To Find : Root of  equation by secant…

Q: E prove that - Cotx + C 2 |- Cosx +Sinx

A: Solve the integration

Q: Differentiate the following 1. g(x) = x³ cos x 2. g(x) = 4 sec x + tan x sinx 3. g(x) =- 1+cosx tanx…

A: 1) g(x) = x3cosx2) g(x) = 4secx+tanx3) g(x) = sinx1+cosx4) g(x) = tanx secx5) g(x) = x1+sinx

Q: - In-2. Hence show that In = 01 tan" x dx = n - 1

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Q: Assume sin(0) = 12 where 0 < 0 <. Compute the following in terms of x. tan (20) cos (2) - -

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Q: Q4) Prove that dx 1+ 2 sinx || In √3 Χ tan tan x + 2 -√√3 +2 + √√3

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

A: Consider, tanx-tany=sinxcosx-sinycosy=sinx cosy-cosx sinycosx cosy=sinx-ycosx cosy…

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.