. Use Taylor's neries, to prove that ein z tan (x+ h)3tan" % + (h sin z). sin 3z sin 2z + (h sin zj . 2 -1 - (h sin z . | 1 where z = cot

Q: Prove that n r=0 "C, sin rx.cos (n-r)x=2"-¹x sin nx. 1

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Q: 18. Use periodicity to express sec in p given that sin

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Q: 2. Prove the following identity: sin (x+y)sin (x-y)=cos² y-cos²x X =COS - COS¯ x X.

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Q: I'm supposed to make a truth table for the premises and the conclusion shown in the photo. I'm…

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Q: prove that 2. = - Cotx + C 2 |- Cos?x + Sinx

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Q: sin r 4. Compute J r(I) dr.

A: Evaluating the given integral.

Q: 8F OF OF 1. Use the formulas above to find and ду ax exy + sin (xyz) + In (yz) = 4 – z

A: Partially differentiate the function with respect to x.…

Q: Compule he an Curvc given aM byO x= and ye 3tcos(t) 'from DLtL engh ot M pacbmeter 3t Sin (t)

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Q: ) Prove that tanh'x = tn/itx, X€ (-1,1) i) , Sinh 'x and tanh'x Find the derivative of coch'x

A: (1). We have to prove that:   tanh-1x=12ln1+x1-x

Q: Use the addition formulas for sinh x and cosh x to prove tanh u + tanh v tanh(u + v) = 1+ tanh u…

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Q: tan 6= .and 0s@s90 , then sin 0- O V3 2. V5

A: Solve for sin theta

Q: Differentiate a $sin "(z) with respect to sin x.

A: We will find out the required value.

Q: Apply Newton’s approx. to find the value of x for cos x = tan x; x0 = 1.

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Q: y(x^2 y^2 - m)dx + x(x^2 y^2 + n) dy = 0

A: yx2y2-mdx+xx2y2+ndy=0Let M=yx2y2-m∂M∂y=y·2x2y+x2y2-m        =3x2y2-mLet N=xx2y2+n∂N∂x=3x2y2+nNow,…

Q: 7 |sin? xdx 2 |sin? xdx 11 Ssin? xdx

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Q: 3. For any z = x + iy € C, prove that |sin z|? = sin’ x + sinhy.

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Q: Let x² + sin(yz) = xz² + y dz and ду dz Find

A: Given,           x2+sinyz=xz2+y

Q: Let n be an element in Z. Prove that 5|n^2 if and only if 5|n.

A: If n be an element in Z. We have to prove that 5|n^2 if and only if 5|n.

Q: 16) Prove the 1+ tan?(u) = sec2(u).

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Q: III) Prove: 2) cos x x + sin æ sin y = sin 3y (3) COS (2) for all x and y such that x+y= 2

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Q: 10. Integrate the function. 8 ip- 1+ 641 2 sin" 8 2 2 tan- 8 2 tan" 8

A: We have find the integral.

Q: What is the trigonometric substitution that you would use to evaluate the integral S V5x2 + 10x +…

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Q: T/2 TT/6 sin x 2 1.)Prove that

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Q: 2. Prove the following identities. = tan (x+2) 1tanr 1-tanx b) sin(π-x) - tan(-x) = sin2x c) secx =…

A: By the answering guidelines of Bartleby, We can answer only first three subparts, please post other…

Q: cos ax -dx = te' 2 х* +1 ле",а 20.

A: In this context, prove ∫-∞∞cos axx2+1dx=πe-a,a≥0. Consider, ∫cfzdz=∫-∞∞cos…

Q: 1. If Z = sin r+ 2 I+1 6. - ", find dZ/dr.

A: differentiate with respect to x

Q: Prove that sin? 0 – sin* 0 = cos? 0 – cos* 0. cos“ 0.

A: We can use the trigonometric identity, sin2θ+cos2θ=1 sin2θ=1-cos2θ.