1) sinh-1x = In(x + Vx² + 1) %3D 2) cosh-1 x = In(x+ Vx² – 1) %3D 3) tanh-1x In ) X = 1-x

Q: D?/if w= Cos (X+y)+Sin (X-y) Show that

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Q: sinhx dx 1+ coshx ) A 1+ coshx B (1+coshx)? (1+coshx)² D 1+ coshx

A: We have to find

Q: csch-1 x= x = sinh sinh11 X Prove mathematically that the right-hand side is equal to the left-hand…

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Q: dy for the following functions : dx 1. Find 3(x – 1) (ans.: 5) Sec² /2x +7 15) y=\tan /2x +7 (ans.:…

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Q: 2 + sin x Differentiate Y x + cos

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Q: tan(x+1) Find y' of y =

A: y=tanx+1x

Q: et secydx + sinydy = 0

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Q: Salve for x if Arc tan (1- x) + Arc tan (1 + x) = Arc tan

A: Our Aim is to solve for 'x' if tan-11-x+tan-11+x=tan-1x -(i)

Q: d 1+ sin² (2)| dz

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Q: aresin (2x-1) = 1-x 2 arctan

A: Substitute x = cos^2(theta) and simplify the equation.

Q: x* + 4 dx : %3D 3

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Q: x' sin (tanx*) -1 Integrate 1+x

A: Introduction :

Q: In(cosh x + sinh x) + In(cosh x – sinh x) = - 1 -1 Leave Question 2.

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Q: y = In (3²×) + sec (Inx²) + tan¬1(In5x)

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Q: Verify the identity cosh 2x = cosh2 x + sinh2 x

A: we have to verify the identity: cosh(2x)=cosh2x+sinh2x   L.H.S: cosh2x as we know that coshx=ex+e-x2…

Q: Show that z- sinh z Rcs :* sinh z

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Q: 6(2tanx - x^4 + 4lnx)^1/4(2sec^2x - 4x^3 +4/x)dx. Hint: let u = 2 tanx - x^4 + 4lnx

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Q: Differentiate, hcx) = In (x-Vr

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Q: dy/dx for (ln(tan(2x)-sqrt(3+e^2x) / (pi(x)^3-cos^2(-5x))

A: Given,     y  =  ln(tan2x)-3+e2xπx3-cos2(-5x)

Q: Differentiate: y= tan(8x2-3x*) %3D O y' = (16x - 12a) sec(8a? - 3x*) tan(8r2- 3r) O y' = (16x – 12a)…

A: Given; y = tan(8x2-3x4)

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.