If w=f(a,b,c)=cos(ab)sin(b)+c, what is at ( -,6

Q: 10. Since (7,-1) is a point on f (x) cos z,which point will be found onf'(x) = cosx ? %3D O a (1,ח)…

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Q: Cos x = Cos" x 1-

A: In this question we have to prove cosx=cos-1x.

Q: (b) Prove that : - 1) (coshx)2 – (sinhx)2 = 1 ,2) coshx- sinhx = e-*, 3) (cothx)? -1= (cschx)?

A: Given that  The following

Q: tan(v) In(cos(v))dv.

A: Assume lncosv = t Differentiate both sides

Q: Prove that cos(sinx) = /1 – x².

A:

Q: ) Prove that 2+sinZA Cos A-SinA

A: To Prove: cos3A-sin3AcosA-sinA=2+sin2A2

Q: If 16(sinx)2 + 16(cosx)² 10 then x=.. %3D Зп/4 T/2 п/4 T/3

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Q: e cosl – i e™ sin 1 + e¯ cos 1 - i e- sin 1 2 e cosl + i e™ sin 1 – e- cos 1 + i e¯I sin 1 -TT 2 e…

A: Simplify the given expression: Coshπ-i

Q: 9) -135° Pos Neg Sin Cos -:-

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Q: if f(2) = zsin(z) -1 defined on the interval (2. 3] then es using False-Position method equals [x in…

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Q: Find the areg between Ye CosX an d y--SinX trom o tr .

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Q: Show that Cosx dx 9- Sin 3D

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Q: Since the functions y cos(x) and y -1 = cos are inverse functions, explain why COS (cos(-)) is not…

A: use the range of arc cosx to find the values

Q: E prove that - Cotx + C %3D 2 |- Cos?x +Sinx

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Q: If * = 2 tan(0), then a. cos(0) Vx2 + 2 Ob. cos(x) = Vx2 + 4 c. sin(8) = Vx2 +4 O d. cot(0) 2 е.…

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Q: x'+y° Q4. If u = sin- sin-'( -), Show that x+y ди X- ди + y- = 2tanx (2 + ду

A: If u=sin-1x3+y3x+y, then show that x∂u∂x+y∂u∂y=2tanx.

Q: Find if r = sin[cos(-0)]. de dr = sin 0 cos(cos 0) de dr cos[sin(-0)] de Option 3 Option 1 dr dr sin…

A: This question is based on application of Derivative.

Q: 4. Evaluate et cos xdx.

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Q: Show that 3(sinx-cosx)*+6(sinx + cosx) +4 (sin r+cosx) = 13

A: Since multiple questions are asked, Answering first one. Repost with other question if you want to…

Q: Compute : exp(i sin(e-i))

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Q: Let S(x) 9 sin x + 9 cos x "(x) 3= r(-)-

A: A function is given as fx=9sinx+9cosx. The objective is to find the first derivative f'x of the…

Q: Suppose that π≤θ≤3π/2, tan(θ)=6/12, find sin(θ)=______. (round to 3 decimal places)

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Q: Use Simpson's rule with n = 6 to approximate cos(x) rp-

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Q: Prove that the equation sinx = 0.3 has at least one solution in the interval(o, π/2).

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Q: y cos?£ 1-CUSE tanzz

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Q: 7. B- Show that: (1) lime-0 tan 8 (2) tan 0 sec20 =D1 %3D do

A: Solve

Q: Calculate ∫9sin^4(x)cos^2(x)dx

A: Given: ∫ 9 sin4 x cos2 x dxFormula: cos2 x = 1-sin2 x…

Q: 3. In (cose) tane de

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Q: Why is V /5+ 5 tan² 0 = v5 sec² 0? Because Vtan 0 = sec 0 Because 1+ tan² 0 = sec² 0. • Because sec?…

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Q: Show that sin , +sin ¤, = 2 cos[;(4, – Þ,)]sin[;(P, +Ð,)]

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Q: If cos(x)=sin(x)=0.5 , find the following:   1) (sec(x))^3 2) sin(2x)+(cos(x))^2 3)…

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Q: Compute (sin (x)) dx cos'x 3 sin' x cos x O Not listed here 3 sin? x 3 sin x cos x

A: Given query is to find the derivative of the expression.

Q: show that1) d/dz [cosz] = -sin z , 2) 1+tan2 z = sec2 z

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Q: Show that 3(sinx-cosx)*+6(sinx + cosx)²+4 (sinºx+cos°x) = 13 %3D

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Q: Find , if da y = 3x cos4x 12x* sin4x – 10x cos4x None -2x4sin4x – 12x° cos4x -12x4 sin4x + 12x°…

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Q: if / 2³3 rsin rda -x³ cos x + 3x² sin x + 6x cos x Oxsin x O cos x sin x X COS X = 6 ƒ ƒ(x)dx, then…

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Q: Use Simpson's rule with n = 4 to approximate /" cos(2) -dr

A: Given: ∫16cosxxdx Here a=1, b=6 and n=4  h=b-an∆x=6-14∆x=54∆x=54

Q: Show that cos(arcsinx) Vi - x², for x| s lin two different ways.

A: Show that cosarcsin(x)=1-x2, for x≤1

Q: Show that sin²(x) cos(x) = sec(x) – cos(x)

A: We need to show the following. So,         Manipulating right side=secx-cosx=1-cos2xcosx=sin2xcosx

Q: If x is measured in degrees and f(x) = cosx, then d f(x) = − sinx

A: To write that it is true or not.

Q: sin(x - ) = -COS X 2

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Q: Let w- fx.y.) - :), x- cos(), y sin(» and :. Then:

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

A: Solve the integration

Q: is it right to say cos (60o-30o) = cos60o .cos 30o+ sin60o.sin30o?

A: cos(A-B)=cosA.cosB+sinA.sinB

Q: S- cos ve ve sin? ve de =

A: We will evaluate the given integral.

Q: If sinx = siny = a and cosx = cosy = b,then cos(x-y) is

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.