Problem E4 Proof that: cos³x+sin³ x cosx+sinx + cos³ x-sin³ x cosx – sinx = 2

Q: 1 + sin 4x cos 4x + C 8. 13.

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Q: COS (+3 O cos x Ocos 2x O sin a Ocos z +x) + cos (-) is equivalent to:

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Q: √3+2 px/3 ² √²³ (2² 10 (2 cos 0 - 3 sin 30) de dr

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Q: r=2(9+1)sin0

A: Since  Sin (0) = 0

Q: Show that sin-1 v + cos-1 v = π/2 .

A: Given: sin-1 v+cos-1 v=π2

Q: -co e-tsint (1) Evaluate f tsint dt t

A: Given integral is ∫0∞e-tsinttdt. Evaluate the integral ∫0∞e-tsinttdt.

Q: If A = A-1 = 2e2t sin(5t) 2e²t cos(5t) 2e5t cos(5t) -2est sin(5t) , then 4

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Q: cos x csc3 x + C sin4 x 1.

A: To evaluate the given integral.

Q: dy Find dif sin x + 2 cos 2y) = 1 dx

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Q: -5 sin x = -2 cos2 x + 4

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Q: s 4

A: To simplify (cos 3x)(cos x)-(sin 3x)(sin x)

Q: Show that sin² 0 cos² 0 8 1 cos (40). 8

A: To show that: sin2θcos2θ=18-18cos(4θ) Solution: We know: 2sinxcosx=sin(2x)    ..(1)cos(2x)=1-2sin2x…

Q: What are the differences between cosx and cos ¹x

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Q: d. Show that sin 8x + sin 4x cos8x-cos4x = -cot(2x)

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Q: If cos a + cos B= a and sina + sin B= b, then show that 2 sin 2a + sin 2B = 2ab 1 a2 + b2

A: given: cosα+cosβ=asinα+sinβ=b we have to show that  sin2α+sin2β=2ab1-2a2+b2 R.H.S: 2ab1-2a2+b2…

Q: COS 437/12 COS7T4+Sin 43T112 Sin? Ti/4

A: The expression is given by cos43π12cos7π4+sin43π12sin7π4 To evaluate: The value of the expression

Q: -1 1

A: Given that cos(arcsin(-1))   we know that arcsin(-1) equal to π/2 or 3π/2

Q: 2-Find L(e-3tsin2t)

A: Given function is, f(t)=12e-3tsin2t Now, from the property of Laplace transformation we get, L(…

Q: Evaluate cos³ (7x) sin(7x)dx

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Q: 2 sin2x – 3 = 3 cos x and 90° < x < 270°

A: Hello , thanks for your question as it is not clear mentioned that it is Sin2 x or sin 2x So we are…

Q: Find cos 0 and csc 0 3 if sin 0 = -- and cos 0 < 0

A: given  sinθ=-34we know sin2θ+cos2θ=1and sinθ=1cscθ

Q: If A = A-¹ = 4e5t sin(7t) 6e5t cos(7t) -4e²t cos(7t) 6e2t sin(7t) ] then

A: Given matrix is A=4e5tsin(7t)-4e2tcos(7t)6e5tcos(7t)6e2tsin(7t)

Q: Question 3 nd /4 (a) Find dt 4 +9t² (b) Use an appropriate substitution to find Ső 0 sin x cos xe²…

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