1 Show that L-1{ = (sin hat sin at) s4+4a4, 2a²

Q: Suppose that x = cos 0 . Find an expression for sin 0 in terms of a 9 4 z2 6,

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Q: Q4:B/Simplify [cos 40+ i sin40 1³ [cos 20-i sin2015 using De Moivre's theorem?

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Q: Q4:B/Simplify [cos 20-i sin2018[cos 30+ i sin301² [cos 40+ i sin40]³[cos 20-i sin2015 using De…

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Q: If +a= a(2 cos 0 cos 20) and y=a(2 sin0 sin 20),show that (z² + y² + 2az) = 4a² (z² + y²). %3D

A: Given that, x+a=a2cosθ-cos2θ⋯⋯1y=a2sinθ-sin2θ⋯⋯2 Squaring both sides of (1) and (2) and adding,…

Q: Q3) Ify = in[sec 8 + tan 8) find

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Q: Find sin 2x, cos 2x, and tan 2x if sin x - and x terminates in quadrant II- sin 2x %3D cos 2x %3D…

A: Use the fact that in second quadrant cos and tan are negative.

Q: Show that (1-)dy+(cos xsin x-sy")dr =0 is an exact equation. Hence, find its general solution. Hint:…

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Q: Find sin 2x, cos 2x, and tan2x if tanx = and x terminates in guadrant II. sin 2x ? cos 2.x tan 2x…

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Q: Suppose that places) < 0 < 2T, csc(0)=8/3, find sin(0)=___. 2 (round to 3 decimal

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Q: Show that L-1{ = (sin hat sin at) s4+4a4, 2а2

A: To find Inverse Laplace transform of ss4+4a4: write ss4+4a4 as  ss2+2a22-2as2 Then the denominator…

Q: Express the 10th term of ( x1 + x2)º in terms of sinusoidal functions (sin, cos).

A: The expression is x1+x220. As we have obtained…

Q: (a) Show that the equation cos rdr + (1+ -(+)- sin rdy = 0 is not exact.

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Q: is there a proof that cos^2t +sin^2t=x^2 + y^2 =1 ? if there is , how?

A: To prove the below statement Consider a right angle triangle as shown below

Q: If cos(0) 1 and 0 satisfies T < 0 < , find sin(0). 2 - sin(0) = %3D

A: Given: cos θ=-16 &amp; π&lt; θ&lt;3π2 To determine: sin θ

Q: Q4:B/Simplify [cos 20-i sin2018 [cos 30+ i sin30 1² [cos 40+ i sin40 ]³[cos 20-i sin2015 using De…

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Q: 5. Find y', if y = 2cosx sin2x – sinx cos2x %3D

A: NOTE:according to company rules I need to solve first question when multiple questions are posted

Q: 6. Evaluate A sin³ x cos4 x dx.

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Q: 1. If z = sin2+In^, find the value of x- +y X

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Q: 3. Express 1++cos2x in terms of cos x. hence a. Evaluate (1+ cosx)dx b. Express 1- cos2x in terms of…

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Q: 10. Show that L(cos- 3t – sin“ 3t)= 36 s2+36

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Q: 8. -dt 1+64t 2 sin-8 B. А. (). -1 2 tan 2 tan- 8 O c. D.

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Q: 5. Find y', if y 2cosx sin2x – sinx cos2x %3D

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Q: 2x 0.9511 and cos 2元 and sec 2x Round to four decimal places. 5. Given that sin- 0.3090, find tan O…

A: Given  sin2π5=0.9511cos 2π5=0.3090we know that tanx=sin xcosxsec x=1Cos x

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

A: Given data,  tan(x)= -(2/3) Where x in 2nd quadrant. A)sin(2x)=? We know that;…

Q: Show that the equation 2x + cos(x) = 1 has exactly one root. (IVT and Rolle's Theorem)

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Q: 1 os( 1 (sin(7z))* =| x)+ cos( x)

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Q: Evaluate the integral. sin (8t + 16) dt cos (8t + 16) sin (8t + 16) dt = cos (8t + 16)

A: Solved below

Q: Express f (0) = cos 20 + 4(sin 20)² + 1 as a sum of powers of sin 0.

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Q: d. Show that sin 8x + sin 4x cos8x-cos4x = -cot(2x)

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Q: (i) Prove that sec 3x(sin 3x-2sin' 3x)= tan 3xcos 6x. (ii) Hence find, for 0s.xs, the values of x in…

A: Trigonometric equation

Q: 9-10.j Show that sin20 2tane %3D 1+tan20

A: We will prove the trigonometric formula.

Q: Evaluate x2 dx Select one: on O(sin (2r- 1) + 2(2 (2ain (r) + sin(2si To (stn(2 1I) 2(2r sin(2sin

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Q: Prove (Start either from the LHS or the RHS but DO NOT work from both sides at the same time) 1.…

A: sin2x=1-cos2x and,  tanx= sin(x)/cos(x)

Q: 10. Integrate the function. 8 -dt 1+ 64t 2 sin- 8 O A. В. 2 tan- 8 2 tan- 8

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Q: e). Prove that Sin3A+sinA 25in2A -COSA

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Q: Activity 2 Differentiate the following. 1. y = sin(6x) 2. y = sin (5x – 2) 3. y = tan (2x³ + 5) 4. y…

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Q: Prove that 3x Question 4 (i) sin(tan-(3x)) cos(tan-(3x)) = 1+ 9x² d 1 (ii)- sin-'(/) = dx 2a/1 – x

A: A detailed solution is given below.

Q: 9. Prove that | sin n0/sin 0| <n, limiting values being used when sin e = 0.

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Q: The suitable substitution to evaluate | sin 4(x+2) dx is None (1- cos8(x +2)] [1- cos4(x + 2)]…

A: Given that: ∫sin24(x+2)dx

Q: Evaluate 1) S sin ³x cos³x dx

A: Given: ∫sin3(x)cos3(x) dx

Q: 6. In right ALMN with right angle at N, sin L 4x-0.22 and the cos M 2x+ 0.28. Determine and state…

A: Given; sin=4x-0.22 and the cosM =2x+0.28.

Q: Show that : |sin x |= CoS nX Σ n2 even 414 2/7

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Q: Find sin 2x, cos 2x, and tan 2x if sinx= and x terminates in guadrant IV. sin 2x %3D cos 2x %3D tan…

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Q: 6. Show that in the interval (0, 7) 4 cos 2nx sinx = 元 Σ 4n2 -1

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Q: b) Is S cos4xV2 – sin4x dx (2 – sin4x)³ + C true or false? show me

A: this is false because

Q: Suppose that 3π/2≤θ≤2π,  csc(θ)=11/4, find sin(θ)=______. (round to 3 decimal places)

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Q: Show that 1 − cos x = x2/2 with an error less than 0.003 for |x| &lt; 1/2.

A: Given: 1-cos x =x22;    |error|&lt;0.003Formula:  The…

Q: Suppose that π/2≤θ≤π, sin(θ)=2/9, find cos(θ)=______. (round to 3 decimal places)

A: Here, θ is in the second quadrant( π/2≤θ≤π) and cosine is negative in the second quadrant.

Q: 7. Prove that: ++) + sin; + e) = v3cose (3) (a) COS

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