sin2 x cos2 4. sin x- cos4 x X - - 1 4

Q: Establish each identity.

A: The given identity is,  1-cos θsin θ+sin θ1-cos θ=2 csc θ The objective is to establish the…

Q: cos (x sin )=√₁ (x)+2 J₂ (x) cos 26+2 J₁ (x) cos 44+... sin (x sin )=2 J₁ (x) sin +2 J, (x) sin 36 3…

A: Using generating function of Bessel functions

Q: 3 sin x + 4 cos x +5**

A:

Q: sin(2r) dr 9- cos (2.x)

A: Integrate

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A: We are given trigonometric equation as

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A:

Q: 1+ sin(x) cos(x) 1+ sin(x) = 2sec(x) cos(x)

A: on solving this

Q: sin 2x 10. Simplify 1-cos x (a) 2cot x (1+ cos x) (b) sin 2x (1 + cos x) (c) sin 2x (d) – 2 tan x (1…

A:

Q: Sin 0/1 + co² B) 2.

A: sinθ1+cot2θ                             =sinθ1+cos2θsin2θ…

Q: sin 0- cos 0+1_ sin0+1 sin 0+cos0-1 (c) cos e

A: consider LHSLHS=sinθ-cosθ+1sinθ+cosθ-1multiply and divide by cosx LHS=(sinθ-cosθ+1)…

Q: 7. cos 2x- cos x -2 = 0

A:

Q: sin(3x) cos(6x) – cos(3x) sin(6x) = -0.6 X =

A: There is trigonometric identity sinA-B= sinAcosB-cosAsinB

Q: 2. 5. xcos x (sin'x - 2sin'x + sin°x)(cosx)

A:

Q: Verify the identity.

A: 2cos⁻¹x = cos⁻¹(2x²-1) , 0 ≤ x ≤ 1 RHS = cos-1(2x2 - 1)Let cos-1(2x2 - 1) = AcosA = (2x² - 1)cosA +…

Q: cos 0 sin 0 0 - sin 0 cos 0 0 1

A: Here we get one real and two complex eigenvalues. We calculate eigen vector only for real…

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A:

Q: 65. 3 sin x = cos x 67. cosx- sin²x = 1 69. 2 cosx- 3 sin x- 3 = 70. 2 sin?x - cos x - 1 = C

A: 67. cos2x - sin2x =1 1 - 2sin²x = 1 Cos2x =1 2x = cos-(1) 2x = 0, 2π , 4π ..... x = 0,π,2π  So…

Q: Cos 3.x - cos 7x 53. sin 7x + sin 3.x cos tan 2r 54. sin = %3D

A: We can verify question no 53 as below

Q: sin(0) = - 2 V3 csc 0 = 2. cos 0 = -. Cos O sin 0 cos 0 = 0.

A: Please refer the attached image for complete solution. THANK YOU.

Q: 4. sin(4x) = (4 sin(x) cos(x))(2(cos(x))² – 1) %3D

A:

Q: sin x - cos x = 1/5, what is (sin x) (cos x) equivalent to?

A:

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A:

Q: cos(x1)=-1/3 sin(x2)=2/3 find 1. sin(x1+x2) 2. cos(x1+x2) 3.sin(x1-x2) 4.cos(x1-x2)

A:

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A:

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A:

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A: cosx-11+cos-x=-sin2x

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A: Use trignometric ratio and identities:-

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A:

Q: 1-T= 3- Z= +cos(y)tan ( √x-b cos (n) 2-sin²(n) 2-B=sin(x) sec(x)/cscf(x) 4-(w+n)²(a+) x-3

A:

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A:

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A:

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A:

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A:

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A:

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A: Trigonometric ratios

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A:

Q: 2 2. (sin cos x) = sin 2x +1 2х +

A: The given identity

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A: we have to prove

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A:

Q: 4 sin x cos x + 2 sin x - 2 cos x - 1 = 0

A: first factorize the given equation and than split two product equation  detailed solution is given…

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A: Topic - trigonometric Equations Put cos 2x = 2 cos2 X-1

Q: 6(cos² x – 1) sin a cos x – sin x O 6 sin æ + 6 cos e O 6 tan x + 6 sec x O 6 tanx +6 csc x O 6 cot…

A: We need to simplify the following expression 6cos2x-1sinxcosx-sinx

Q: cos(x + =) – cos(x – ) = 1 6. cos ( x 6. 6.

A:

Q: x(1+x?) sin x+ cos x + x² cos x – x cos x (1+ x³)% = (1+x?)?[cos x– x(1+x?)sin x]

A: We want to prove that both equation are equal.

Q: 1+2 sin x cos x 1-2 cos2 x sin x+cos x (d). sin x-coS x | |

A:

Q: sin-1 x = cos s-'(1 – 2x²) x > 0. |

A: The above problem is solved.

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A:

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A:

Q: 1- sin(x) A cos(x) +x+C COS 1+ sin(x) B -x+C cos (x): cos(x) -+C cos(x) – x 2cos(x) D 1+ sin(x)

A: