Prove the identity. 5 tan(3x) = 15 tan(x) – 5 tan²(x) 1- 3 tan?(x) Rewrite 3x as 2x + x and use the Addition Formula for Tangent to simplify. 5 tan(3x) = 5 tan(2x + x) 1- tan(2x) tan(x) Use the Double-Angle Formula for Tangent to simplify. + 5 tan(x) ctan(x)) 19 + 10 tan(x) (1 – tan (x)) – Need Help? Read It Watch It

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: 14. Find the smallest positive root of tan x+2 tanh x = 0.

A: Newton Raphson Method:- The root is xi+1 =xi - fxif'xi; i=0, 1, 2, ....   Given equation is tanx +2…

Q: sin 0 + In + 22+3 = -3 - cos 20 - In y? + 327-4 = + 2ln y+ 22 -3 1+ (cot 0)2

A: Given system is sinθ+ln1y+2z+3=-3 lny2+32z-4=1-cos2θ2 21+cotθ2+2lny+2z=-3

Q: .2 -If tan -1 = 0, then prove that x2 sin 2 a. %3D

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Q: 10- Sin'x- cos'x is equal to: a)2x b)1 c)-1

A: 10-sin^2(x) -cos^2(x) We apply trigonometry rule

Q: iV. Prove that tan50 t5-10t3+5t where t tan0. Deduce the values of 5t4-10t2+1 tan for n 1,2,3,4.

A: Consider the given information: To prove that tan5θ=t5-10t3+5t5t4-10t2+1,   t=tanθ

Q: -1 3. Show that sin-¹x = tan X √1-x² if |x| < 1.

A: Introduction: When there are trigonometric functions present in an expression or equation,…

Q: 4. cos*x Evaluate: sin' x( sin' 3/5 x+ cos³ x 3.

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Q: 8+tan x dx 1-sin?x i.

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Q: Verify the identity:

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

Q: sin 2x 10. Simplify 1-cos x (a) 2cot x (1+ cos x) (b) sin 2x (1 + cos x) (c) sin 2x (d) – 2 tan x (1…

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

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Q: A. Let 0 = 2x, then the identity cos 2x = 1-2 sin2 x becomes cos e = 1–2 sin2 (0/2). a. Use this…

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Q: 4. Find the exact value of cos *x- sin "x-cos (2x). 4 cos x- sinx- cos (2x) = (Simplify your…

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Q: 2 cos(5x) – 5 x² – 2 sin(3x) – x2 – 3x - lim - - (Write your answer in the given box)

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Q: Can you please help me with my verify the identity problem? 1 + sec^2x / 1+ tan^2x = 1 + cos^2 x

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Q: Osl 2. 2Sin x- CosX+1 = 3 tan x 2 Cos?x

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Q: Express sin 20 in terms of x, where x = sin 0. A. sin20 = sin? 0 = x² 2x(1– x² )² C.sin20 =…

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Q: True or false: If tan 3x = any integer n. + nn for 4 1, then x = %3D

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Q: 2. By hand, showing all steps, determine sin 4x sin 5x lim x sin 3x

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Q: III. Verify the identity. 5.) 1-Cos 2x tan?x %3D 1+ cos 2x

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Q: 3-f(x) = tanh¯1(cos(e*))

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Q: 2/2 and <x< 3 Зл find tan 2x. 2' 4. If sin x

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Q: 1. Determine (i) |cos (2x– 7) dx dx (ii) x +9 (ii) dx 4-9x² 2. Determine (sin x cos x dx using (1)…

A: Since, you have posted multiple questions we will only first question with three subparts as per our…

Q: 2 cos (x2) - 4x 2 sin (x2)

A: 2 cos (x2) - 4x 2 sin (x2)

Q: Verify the identity. 6 cos(sin-1 x) = / 36 – 36x2 Let 0 = sin-1 x = sin 0 = x = X. Thus, 6 cos(sin-1…

A: use trigonometric identity  to verify it.

Q: 3x2 sin(x³) Select one: а. In/tan x3 + cot x³| + c b. -In csc x3 + cot x³| +c С. с. In|sec x3 +tan…

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Q: - sin sin -y = sin (x+y) Prove that cos Xcos 4 -y 4 -x sin 4 X - 4

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Q: Find all values of x in the interval [0, 27] that satisfy the equation sin x sin x tan x

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Q: 5) f(x) = tan [In{sin(15x - 30)}] %3D

A: For this problem we have to apply derivation to each term.

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

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Q: 6. Approximate the real root of x – cosx = 0 to three decimal places. Let xo = 0.8 and find x1, x2,…

A: Let f(x) = x - cos(x) x0 = 0.8 By using the Newton-Raphson method to approximate the root,…

Q: 12 Find sin 2x, cos 2x, and tan 2x if sin x=- and x terminates in quadrant IV. 13 sin 2x %3D cos 2x…

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Q: sin 0 + In + 22+3 = -3 1- cos 20 In y? + 322 - 4 = + 2ln y + 22 =-3 1+ (cot 0)2

A: Given system is  sinθ+ln1y+2z+3=-3 lny2+32z-4=1-cos2θ2 21+cotθ2+2lny+2z=-3

Q: 1 sin(2.x) = -sin(2x) -125 %3D (D²-1)' true false

A: Solution

Q: 1– tan(*,) [1– sin x] lim 1+ tan(x (¥2) [z – 2x] x- - 2 1/8 1/32

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Q: 12. sin 2t – tan t = tant cos 2t - HINT: You will use a reciprocal identity.

A: use the formula

Q: 2. tan 2 7 with 180° < I< 270° 3 given tan x

A: It is given that

Q: lim,-o-cos(2.x) →0°sin²(3x) Q6- Evaluate:

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Q: 2. cos(4x) = 1 – 8(sin(x))²(cos(x))²

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Q: 1/4 (1- tan x) (1+ tan x) Q.37 dx evaluates to

A: Introduction :

Q: 5. sin 2 x=cos X

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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: 3+(e*+3) sin x %3D tan(x³)-x

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

Q: tx)+ Sin(꼴-)- -26S X %3D Prove sin

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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: 5(cos²æ – 1) sin x cos x sin x - ||

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

Q: x) - 0.5 cos(x)) on the

A: Given as, f(x)=e-x3.2sinx-0.5cosx in the interval [3, 4].

Q: 7. Prove the identity. – sin 3 TT -x= 0 2 sin +x 2

A: