c) sin'0 (1+cot)+cos' e-(1+tan 6)=sin+cos d) tan' @ 1+tan¹ 0 cot' 0 1+cot¹0 + 1-2sin² @cos²0 sin cos

Q: IRI- 2. <| sinz|< -e 2

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Q: Establish each identity. as attached.

A: Assume x=2u in the equation cos2(2u)-sin2(2u)=cos(4u) that will be cos2(x)-sin2(x)=cos(2x) and than…

Q: sec 0 cot 0 –sin 0 = cos 0 cot 0 Cos e cot 6 %D

A:

Q: 1+ sin 0 csc0+1 1-sin 0 csc0–1 II

A: We have to prove the identity.

Q: Establish the identity. 1 1 = 2 sec20 1- sin 0 1 + sin 0

A: Given query is to find the correct statement.

Q: sinx - cosx + 1 sinx + 1 %3D Hint: the conjugate of the denominator sinx + cosx - 1 is sinx + cosx +…

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Q: Establish each identity given in attachment.

A: Given equation: asinθ+bcosθ2+acosθ-bsinθ2=a2+b2

Q: Prove that ABC and EDC are similar

A: In triangle ∆ABC we have given  AB=3, BC=5 and CA=4In triangle ∆EDC we have given  ED=9, DC=15 and…

Q: Prove that 1 + 2 + 22 + 23 + . + 2 2n-1 1 for n2 1. Use proof by induction.

A: Given  1+2+22+23 + . . . + 2n = 2n+1-1 for n≥1.

Q: Given and prove

A: Given,

Q: sin OCose 1- cos 0 1+ Cose Tane

A: Proceed as shown below...

Q: 12-4 If M and N are similar matrices (that is, N = some nonsingular matrix P), then oe(N) = oe(M). =…

A:

Q: Let a, b, and c be natural numbers. Prove a ∙ (b + c) = a ∙b + a ∙ c.

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Q: Establish each identity. as attached.

A: We know that, tanA+B=tanA+tanB1-tanAtanB        ⋯⋯1tan3A=3tanA-tan3A1-3tan2A      ⋯⋯2 We have,…

Q: Establish each identity given in attachment.

A: Given: The identity cos3π2+θ=sinθ The given identity  can be proved as,…

Q: COSX CSCX= cotx

A:

Q: 8) Suppose A E Mnxn(F) is diagonalizable. Let A1,· , Ak be the (distinct) eigenvalues of A. a) Prove…

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Q: Establish each identity given in attachment.

A: Given equation: sinθ-cosθ+1sinθ+cosθ-1=sinθ+1cosθ

Q: (JX K.k).K = 0 (J¹Xk.K) k = 0 aj Əxx.x = JX, K.K

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Q: Prove that the identity is true.

A: Given a). b).

Q: 3. tanB + cotB = cscBsecB

A:

Q: If all entries of A and A -1 are integers, prove that &lt;let A = 1 or -1. Hint: What is det A times…

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Q: Establish each identity given in attachment.

A: To prove an identity we must start with one side of the identity and transform it to the other side.…

Q: () 2p n! (a) (") = 2 (mod p), where k for 0 <k <n. k!(n – k)! (b) (Зр - 1)! 2р2 (mod p3)

A: As per our guidelines we are supposed to answer only fast question. Kindly repost other part in the…

Q: cos 40 8cos4 0 – 8cos² 0 +1 -

A: To prove:  cos4θ=8cos4θ-8cos2θ+1     Solving the right hand side of the equation and taking…

Q: 3. Let n e Z be nonzero and even. Prove that there exist unique a € {0, 1}, b € N, and odd c€ N such…

A: Since n is even and non-zero . Since n is non zero ⇒ n is either positive or negative. Let's write…

Q: Establish each identity given in attachment.

A: The given trigonometric equation is sinθcotθ+tanθ=secθ

Q: Establish each identity given in attachment.

A: To Establish the identity given in attachment. 1+sinθ1-sinθ=secθ+tanθ2

Q: cos 40 = 8cos4 0 – 8cos² 0 +1 -

A:

Q: Prove that ala for all natural numbers a.

A: Details attached as step 2.

Q: 3022.50l cot(-0) = - cot(0)

A:

Q: is called the multiplicative identity. • 0 -1 • 9 • 1

A: The multiplicative identity is 1because multiplying a number by 1 leaves it unchanged . If a is any…

Q: Prove the identity of both.

A:

Q: 2) Verify that each equation is an identity. 1– sin? 0 a) %3D = cos 0 Cos e

A: