Evaluate the in tegrol : S sin 5x cog3 5xdx

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A: Given:sinx=0.3

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A: we have to solve the integral

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A: given that                                                                             coshx=csc2θ…

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A: Formula Used: We will need following binomial expansion:

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A: Consider the function, fu=tanu2+cos2u

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Q: Show that cosh iθ = cos θ,

A: We know that  coshx=ex+e-x2 and by Euler's theorem, eix=cosx+isinxe-ix=cos-x+isin-x=cosx-isinx We…

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Q: In the given question, verify the identity:-   sinh 2x = 2 sinh x cosh x

A: To prove  sinh2x=2sinhxcoshx.

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Q: 2. Is trigonometric substitution needed to evaluate /9 - x² dx?

A:

Q: 5. If coshx = csc20, prove that 0 = n+ cothe¬x. [Hint: use identity sin(2a + 2n)]

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Q: (b) в — р2'а, + psin'ф а, + 2pz sin' ф а, sin²o as + 2pz sin*ф а,

A: The complete solutions are given below

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A: Given:1-cos2x/cos2x To simplify we use some trigonometric properties

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A: Since multiple questions are asked, Answering first one. Repost with other question if you want to…

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A: It is given that,a&lt;1, we have to find the value of              ∫0∞coshaxcoshxdx

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Q: (4) |sin² 0 cos0 d0

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A: we have  sinh(x)=ex-e-x2cosh(x)=ex+e-x2

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A: the given integral,        ∫tan(4x+3) dx

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A: Given : (sin ax)(cos bx)

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A: Let's expand x cos(x ) , xcosx=x1-x22!+x44!-x66!+...=x-x32!+x54!-x76!+...             in 0,x To show…

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A: Recall: ∫1xdx=ln(x)+C

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Q: How do you evaluate ∫ sinmx cosnx dx if m is odd? What if nis odd? What if m and n are both even?

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A: SOLUTION-

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Q: Hint: the conjugate of the denominator #svon sinx - cosx + 1 sinx + 1 %3D xS200is sinx + cosx + 1…

A: