sin 0 + In + 22+3 = -3 1- cos 20 In y? + 322 - 4 = + 2ln y + 22 =-3 1+ (cot 0)2

Q: (1+iV3)"+(1-i/3)" %3D 2n+1 Sin(- 3 2" Cos( ) 3. 2n+ Cos( 3. 2" Sin 3. (1-V3

A: Kindly go through the solution and let me know in case of any doubt or further clarification in the…

Q: sin 20 5) Verify tan 0 %3D 1+cos 20

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Q: Establish each identity.

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Q: Establish each identity.

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Q: sin 0 + In + 22+3 = -3 - cos 20 - In y? + 327-4 = + 2ln y+ 22 -3 1+ (cot 0)2

A: Given system is sinθ+ln1y+2z+3=-3 lny2+32z-4=1-cos2θ2 21+cotθ2+2lny+2z=-3

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: 2) sin- 0 4) cos 6) cos-1 | V3 8) tan 3 -1 -1 10) cos

A:

Q: cos²x 6. 1+ sin x = 1- sinx tanx - сotx 7. sec'x - csc?x = sin xcosx 8.1 tin cos2x = cscx - secx…

A: We have to verify that the given trigonometric identity.

Q: he interval [0,2r) cos (x) sin (x) = 2 cos (x)

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Q: sin(2x) cos(2x) Prove sec(x) sin(x) cos(x)

A: Trigonometry

Q: tan (0) +1 1) sec(e) = sec(0) cos(@) +1 2) tan (0) cos(@) sec(@)-1

A: See the details solution in below

Q: 2 1. sin 0 == and sec 0 > 0 2. sece = - and tan 0 > 0 3

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Q: sin(8x)cos(4x)+cos(8x)sin(4x)

A: We will find the value of the given trigonometric expression in the following step.

Q: plutions of the equation in the interval [0, 27). cos 4x sin 5x - sin 3x - 1 = 0

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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 2x cos 2X I+ 3 cos4X

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Q: 1- cos 0 + sin 0 sin 0 2 csc 0. 1- cos 0 |

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Q: sin 20 + 2 cos 2 0 Verify the identity tan 0 + 2 cot 0 = sin 0 cos 0

A: Solve the given identity

Q: Sin 20 + cos20 +1 Sin 20-cos20 +1 - - сото

A:

Q: establish each identity.

A: Our Aim is to prove sin θ cos θcos2 θ-sin2 θ=tan θ1-tan2 θ -(i)

Q: 11. sin(2 tan-1 (-) 3,

A: A trigonometric ratios sin, cos, tan can take the input in the unit of degree or radians. The…

Q: 4 sin 0-2 csc 0= 0 with 0 degrees

A: We use sin0=0 and csc0=1/sin0

Q: tan20 21-25. Verify = sec?e – sec 0 cose + 1

A: To verify: That tan2θcosθ+1=sec2θ-secθ. Formula used: Trigonometry identity: tanθ=sin θcos θ…

Q: Sinh exp 2 i sin 1 -i sin 1 -i sinh 1 i sinh 1

A: Note the formula:

Q: cscxdx 5+ cos²x sin²x

A: Evaluate: I=∫csc2x5+cos2xsin2xdx We know that, cos xsin x=cot x Then, we have I=∫csc2x5+cot2xdx

Q: sin2 (4) %3D cos2 ( ) O csc2 () csc2 () cos2 ( 4)

A:

Q: 9. sin-1 /2 /2 10. sin-1_ 1

A: We have to find the exact value of the inverse trigonometric expression: 9.     sin-12210.…

Q: sin(5x) dx 2+сos(5x) اخترأحد الخيارات х + tan(5x) + с.ао —In | 2 + сos(5ӕ) | +с.Ь 1 +c.c 2+сos(5ӕ)…

A: Since , in the given integration problem we have derivative of denominator in numerator so we will…

Q: - sin sin -y = sin (x+y) Prove that cos Xcos 4 -y 4 -x sin 4 X - 4

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Q: 2. 2) tan- 1 4) sin- 6) tan-1 V3 -1 01_ V3 10) sin -1 2. 12) tan-! 3.

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Q: √3 csc x − 2 = 0  tan 3x(tan x − 1)  sin2 x = 3 cos2 x

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Q: Ask the paper questions 2-8

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Q: 4. 1-3 cos x-4 cos² x 2 sin² x 1-4 cos x 1- cos x

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Q: Evaluate: lime 1-sin 0+cos 0 sin 20-cos 0

A: The objective is to evaluate the limit.

Q: 2 cos x+3 cos x=2 2 Cos²,

A: Given,   2 cos2x+3 cos x=2

Q: cos 0 - sin 0 tan (-0) = %3D 4 cos 0 + sin 0

A: tan(π4-θ)=cos(θ)-sin(θ)cos(θ)+sin(θ) LHS tan(π4-θ)=tan(π4)-tan(θ)1+tan(π4)tan(θ) [Because Angle…

Q: sec x-1 sin x %3D secx+1 1+cos x

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Q: 3 [cot 0- sec 0- sin 0 O 1 -3 O 3 O 6

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Q: Cos (GX) = Cos 15°, 0°<x < 360° Со X) = Cos 15°, O° < x < 360° %3D Tan( x ) = tan,05x < 2n )= tan,

A: We can find the answers as below

Q: 2 sin(0): 3 Evaluate: csc(-0) = ||

A: sin(θ)=23 To find, csc(-θ)

Q: 2 sin 1 3 -1 cos tan 4

A:

Q: V3 1) tan 3 cos¯1 –1 -1 2) cos-1 | 3) sin- 0 4) tan-' (-V3) 5) tan- 6) sin- 7) cos 2 8) tan- –1

A: tan-133

Q: 61. sec 2 1+ cos 0 65. cos 64. tan = csc v - cot v sin (30) 67. cos (30) = 2 sin 0 cos 0 2.

A: (61) We have to prove, sec2θ2=21+cosθ We know that, from half angle formula cosθ2=1+cosθ2 On…

Q: 1) sin ( sin 3 -1를 + cos-1) 3.

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

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Q: [cos 20-i sin20cos 30+ i sin301² [cos 40+ i sin40 ]³[cos 20-i sin2015 using De Moivre's theorem?

A: We have to solve given Questions.

Q: sin 2 2) = (9z + 4), h(3) (2) (1) = sin(cos r), f"(1) %3D

A: