Prove That 4 Sin ³²A - CoS 3 A +4 Cas³ A - Sin 3 A = 3 Siny A

Q: b) 6(sin x)² + cos 2x + 1 = 0 [0,2π] I

A: Solution6 sin2x+cos 2x+1=0we know cos 2 x= 1-2 sin2xput this value in the given equation,6 sin2 x+…

Q: Prove that the distance sin 0₁ 2³ +|sin 0₂2² + greater than 2/3. of the roots of the equation sin…

A: To prove that the distance of the roots of the equation…

Q: 2) / x² - y²) dx + (x² - ²xy) dy = 0 6 ,2 1 21 COCX

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Q: that "C₁ sin 2x + "C₂ sin 4x + "C3 sin 6x 1+ "C₁ cos2x+ "C₂ cos 4x + "C3 cos E x; where ne N

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Q: c. sin"(t)- cos (t) = 2sin (t)-1 = CS d. cot (2y)+cos?(2y)+ sin (2y) = csc²(2y)

A: Given,  c. sin4(t)-cos4(t)=2sin2(t)-1d. cot2(2y)+cos2(2y)+sin2(2y)=csc2(2y)

Q: Verify sin (x +) = cos(n – x) %3D

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Q: (a) Evaluate the integral using the substitution u = In (5x). x In (5x) dx x In (5x) ? Edit +C (b)…

A: An integral in some cases can be simplified using a substitution. For example ∫ln(x)xdx with the…

Q: PROVE: 1+ sin a 1- sin a CSc a + 1 CSc a

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Q: Prove the following: 1+2sin cos sino + cose = sin 0+ cos 0

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Q: b) sin 3x 3 sin x – 4sin3 x [Hint: sin 3x sin(2x + x)] Prove

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Q: 10. Prove that 7/2 sin 8 cos (cos a cosec 0) de =- (1-cos a). CO TE/2-a

A: We will use the Differentiation under Integral sign method, to solve the problem.

Q: If z = 1+ 2i and w 3+ 4i, express in rectangular form 5 cos [Arg (2²)] + 5i sin[Arg w]

A: The square of a complex number z is the product of z with itself. Multiply 1+2i by 1+2i to obtain…

Q: 18 a Show that / (1 + sin 2zx)dx = n, for all positive integers n. b Sketch y = 1 + sin 27x, and…

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Q: Express 1+ cos a + i sin a in the modulus amplitude form.

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Q: sin2xdx 1) S7 o sin+x+cos4x

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Q: Solve 1- sin (A) +1 2 cos(A) over [0, 27) %3D

A: We have to solve the given trigonometric equation in the given interval.

Q: Solve for x, x in [0, 2Tt). 4 sin 2 x - 4 sin x + 1 = 0

A: Given: 4 sin2x-4 sin x +1=0 , x in [0,2π).          (i) To find: x

Q: Find 1+sin -cos I COS In | sin - z+cos In In 1+tan +C +C +C +C

A: We can evaluate the given integral by using the substitution u = tan (x/2).

Q: QUESTION 2 Je" cos(5x)dx = 7x O A. (7 cos 5x + 5 sin 5x) + C 24 O B. (7 cos 5x – 5 sin 5x) + C 74 e7…

A: Please see the explanation below

Q: cos2t dt Evaluate the Integral (1+ sin2t) 4 A (1+ sin2t) 3+ C (1+sin2t) -3+ C 6. (1-sin2r) 3+ C 6. D…

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Q: Solve the equation for 0 < < 2π. 0 = sin² 0 +2 - 2 cos 0 ○ {0} 0 (7,3,7) 6 ° {{} ° {}

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Q: 6. Prove that: ah cos (i) A sin (ar + b) = 2 sin (ah sin a (ii) A cos (ar + b) = - 2 sin

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Q: = cos 4 + isin and B = cos + i sin. Prove that B is not in Q(a).

A: Given: α=cos 2π7+i sin 2π7; β=cos 2π5+i sin 2π5To prove: β is not in Qα.

Q: Prove that v2 cos(20+45°) = cos e-2sin Ocos 0-sin 0, where 0 is measured in degrees.

A: *formula:- cos(A+B) = cosA*cosB - sinA*sinB. sin2A = 2sinA*cosA. cos2A = cos^2(A) - sin^2(A).

Q: the sum of sin h 2x and cos h 2x

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Q: √ (3(1 + cos 0))² + (−3 sin 0)² do

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Q: 5. Verify the identity cos -(a -B)| COS we sin( B) -

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Q: Sz sin2m-10 cos2n-10 —— В (т, п) 2

A: It is known that, βm,n=∫01xm-11-xn-1dx

Q: Show that n. In(cos 2k+2) = - In (2"+ sin 2n+2). k=0 Hint: sin 20 = 2 sin 0 cos 0.

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Q: উদাহরণ-9. যদি tan c হয় তবে প্রমাণ কর যে %3D - a

A: You need to find the values of sine and cosine of from the given value in the question.

Q: 1 Evaluate Le' cos 2t +÷sinh 2t

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