14) Prove that the following is an identity: (x +y)³ = x³ + 3x²y+ 3xy² + y³

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A: This question is taken from the trigonometry in which we have to prove the given trigonometry…

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A: We have to prove,  HXH = Z ; HYH = -Y ; HZH = X

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Q: 86. Show that Z, = r(cose + isine) and Z2 = r[cos(-6) + isin(-6)] are conjugates. %3!

A: Given,

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A: Given inequality is

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Q: 15) Find The natural domain (a) fx) =3 os X 6 g0) = ©dix) = Sin? x O ra) = 19-x2.

A: given(a)f(x)=3cosxdomain of this function is (-∞,∞)(b)g(x)=13+xx≥0therefore domain is [0,∞)

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A: Using substitution of Cauchy Euler D.E.

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Q: [5] Determine the y(2021) of y=cos²

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Q: Prove that: 1. Z, Z2 =r,r2[cos(8, + 02) + i sin(8, + 02)] 2.4=(cos(0, -62) + i sin(0, – 0,)] %3D 3.…

A: Here we use exponential form to represent complex Numbers.

Q: Photo is attached

A: The given identity is,

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Q: 3. Show that sin? z + cos² z = 1, 2 € C, assuming the corre sponding identity for : €R and using the…

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A: Given a). b).

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A: Follow step 2nd .

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Q: the followking identity. us-1/1+_A Prove

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A: We have to prove thatm+n+1n=∑k=0nm+knProof⇒ As L.H.S is number of subsets {1,....,n+m+1} of size n…

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A: