tan(360°+0)-cos(-0) cos(360° – 0) (a) sin(720°– a)- tan(-a) (c) sin(720° +a)- tan(360° – a) sin(180° – A)-cos(-A) (e) sin(360° – A)-cos(A–180°)

Q: IRI- 2. <| sinz|< -e 2

A:

Q: sin x – 2+ csc x (c) sin x – 1 sin x CSc x sin x + 1 | 1 (d) cos(tan-l x) = V1+ x² 1+cos u (e) Using…

A: We have to answer following Questions.

Q: sin α=3/5, 0<α<π2​; cosβ=(2√85)/85, −π2<β<0   ​(a)   sin(α+β)         ​(b)   cos(α+β)         ​(c)…

A:

Q: sin x cOs x 1 – sin x 2sin x 2 cos x 3 cos x -1

A:

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: 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…

Q: sin (2n-1 ( a) Does Σ-1 converge absolutely, non-absolutely, or diverges. sin(2n-1 (D) Does ΣΗ…

A: Given: ∑n=1∞sin2n-1πnn6 and ∑n=1∞sin2n-1πn5n-3 To find: (a) Whether the series ∑n=1∞sin2n-1πnn6 is…

Q: 8(x²-a²) = 2a (cos - cos 0') [8(x-a) + 6(x + a)], 8(0 - 0′) sin 0 = 8(0-0') sin 0¹

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: sin 5x + sin 3x 2 cOS X 4 sin x cos 4 sin x cos x 3 X COS -

A:

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: solve equation for 0≤ x ≤ 2π. show work.   a) csc x - √2 = 0 b) √2sin x = 2sin x cos x

A: Solve the following equation for x where 0≤θ≤2π cscx-2=0 2sinxcosx=2sinx

Q: sin 0 1- cos 0 = 2 csc 0 1 cos 0 ite the left side of the expression with sin 0(1- cos ) EGO

A: We can establish the identity as asked in the question as below

Q: sin a 4. lim I 1+ cos3 x

A:

Q: Sin 2x- Cos 2.x Sinh (u-v) = Sinh u.Cosh v - Cosh u.Sinh v %3D

A: See the attachment

Q: sin 2a + sin 4a 15. cota %3D Cos 2a - cos 4a

A:

Q: Establish each identity given in attachment.

A: Given equation: sinθ-cosθ+1sinθ+cosθ-1=sinθ+1cosθ

Q: sinx=-3/5, pi<x<3pi/2, and cosB=5/13, 3pi/2<B<2pi, find cos(x-B)

A:

Q: 20. cos x 3 cos x -V2 cos x csc x; xe[0,2n]

A:

Q: sin 0 1 + cos 0 Establish the identity: 2 csc 0 1 + cos 0 sin 0

A: given sinθ1+cosθ+1+cosθsinθ=2cosecθ

Q: establish each identity.

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

Q: (cos x-1)(1+cos(-x))=-sin' x

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

Q: sin (-0) cos² (-0) Establish the identity: cos 0 sin 0 sin (-0) - cos (-ø)

A: Given: sin2-θ-cos2-θsin-θ-cos-θ=cosθ-sinθ

Q: proof : cos4x/sin2x+cos2x=cos2x-sin2x

A:

Q: Prove that

A: Given:d2ndx2nsinx=-1n sinxd2ndx2ncosx=-1n cosx

Q: 4 sin² x - 1 2 sin x + 1 2 sin x - 1

A:

Q: Verify the following identity:

A: We have to prove the following trigonometric identity: sin4x2-cos4x2sin4x2cos4x2=-16cos xsin4 x

Q: tan(x) dx cos4(x) tan'(x) A [7tan²(x) +9] + C 36 1 ℗tan'(x) + tan³(x) + C C D sin²(x)sec³(x)…

A:

Q: (sin 0+cos 0)² 3. sin?0-cos20 sin²0-cos²0 (sin 0-cos 0)²

A: (Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: 6. (a) Express cos (2 tan- ) (b) Express sin (2 cosx) as an algebraic expression in x. (c) Express…

A:

Q: 7. lim a sin(1/a) = %3D a-0+

A: Given lima→0asin1a

Q: cos/ 3 17 cos (TA +x) tanx

A:

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

A: To prove that the left-hand side is equals to the right-hand side.

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: sin 0-2 sin3 0 1. 2 cos30-cose = tan O 1 2. tan? x(1+ coť x) 1-sin2x 1 3. sec ( 2 cos'x) = 2x2-1

A: we have to prove

Q: 3. Using trigonometric substitution, what is 1 sec-²¹ ( 137 ) + √x²-9 2x² + C A. 1 300² (2) √²-90…

A:

Q: cos 0-2 cos 0 sin0 1-sin 0+sin²e-cos²0

A:

Q: tan x a) Prove (sec x – cos x)(csc x – sin x) %3D 1+(tan x)² b) Solve 2(tan x)² – 5 tan x –3 = 0…

A:

Q: sin (x) + cos³(x) = 1 - sin(x) cos(x) sin(x) + cos(x) sin (x) + cos°(x) - (sin(x) + cos(x)) (…

A:

Q: X+1 1-x Select one: a. sin-1(x)-V1-x² +c www. O b. sec-(x)-V1-x? + c C. tan (x)-V1-x2 + C d. cos x)…

A:

Q: cos 2x 25. cos x- sin x A sinx cos X cos x + sin x 2 cos x + sin x cos x - 2 sinx B 2 sin

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…

Q: The value of A. sin-¹ x +√1+ x² + C B. sin ¹x-√√1 + x² + C C. sin-¹ x + √1- x² + C D. sin¹x-√1- x² +…

A: The  given integral is ∫1-x1+x dx The trigonometric identity is expressed as sin2θ+cos2θ=1 therefore…

Q: Using trigonometric substitution to solve: f sin 2x +C 8 cos x√3-cos²x 1 + C 8 secx√4-sin²x sin 2x…

A:

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

A: The above problem is solved.

Q: | ••) sin 30 = sin + = (sin (cos 0) + (cos 20)(sin 0) - (25 2 sin 0. (cos 0) + (1 – 2 sin? 0)(sin 0)…

A:

Q: sin 50 Show that 16 cos 0 – 12 cos² 0 + 1. sin 0

A: given,

Q: Find the limit.

A: We have to find the limit: limθ→0cos θ-1sin θ This is 00 indeterminate form so we can apply L'…

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.