y" - y = 10 cos x cosh x

Q: y'tan x sin 2y = sin² x + cos² y.

A: We need to solve y' tanx sin2y=sin2x+cos2y This can be written as: y' tanx…

Q: tan (x)sın (x)- sın (x)=0 - sin (x)=0

A: Given; tan(x)sin(x)-Sin(x)=0.

Q: (Integral sign) tan^4 x sec^6 x dx

A:

Q: 4. у %3D sec^0 - tan'ө

A:

Q: c) cos x tan x = sin x tanx %3D (Usx.SinzL (os x Sinc sinx cot x + = csc x - CSC X 1+cos x (e Sinzx…

A:

Q: | sin* x cos xdx 4 X COS X

A: This question is related to integration.solve as below

Q: 1. y = 3 sin x – 4 cos x 2. y = x³ tan x 3. f(x) = cos x 1+sinx 4. y = csc x cot x f(x) cin?

A:

Q: sin x cos x) (2 -

A:

Q: 1 - cos(x) y = sin(x) y =

A: Observe the graphs carefully, Figure (b) suggests that the limiting value of the function…

Q: sin(4-y)sin(3-y)dy

A: Use the formula sin(A) sin(B)=12(cos(A-B)-cos(A+B))Consider…

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

A:

Q: If rcos(x)sin(y)=a, rcos(x)cos(y)=b and rsin(x)=c, find r.

A: Formula used is written in the bracket of the first photo.

Q: sinr cos (x - y) - cosx sin (x - )

A: As we know that the trigonometric identities: sinA-B=sinAcosB-cosAsinB   Given:…

Q: sin (x) – cos²(x) Show that 1 F COS %3D CSC (x)

A:

Q: cos 2x – cos x lim sin?

A: To evaluate: limx→0cos2x-cosxsin2x Solution: We know, cos2x=2cos2x-1  ..(1)sin2x=1-cos2x      ..(2)…

Q: verify the identity: sin(x+y) + sin(x-y)         = tanx cos(x+y)+cos(x-y)

A:

Q: cos x - sec x = 0

A: Given equation can be written as Since secx=1/cosx Therefore, we have

Q: i) sin 0+tan 0 1+sec 0

A: Givensin θ+tan θ1+sec θTo findsimplify thegiven tignometric function

Q: y= sin(x + 4) cos (x - 4) y= sec 4x + tan 4x y= Arctan

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

Q: 2 sin(x) cos(x) + v2 cos(x) = 0 COS

A:

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

A:

Q: y = sin* 3x – cos* 3x y = csc* x – 21 cot?x y = cot sin

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

Q: (Integral sign) tan^2 x cos^3 x dx

A: The given integral is

Q: sin 2x 29. sin x cos 2r = sec x cos X

A: As you mentioned solve question no.29

Q: cos(x + y) cosx siny = coty – tanx

A:

Q: 1+sin x/cos x + cos x/1 + sin x = 2 sec x

A: Given:1+sinxcosx+cosx1+sinx=2secx

Q: y = 7 cos(x), y = 7 - 7 cos(x), 0 ≤ x ≤ π

A: The given equations are: y=7cosx, y=7-7cosx, 0≤x≤π To find the area of the region between the curves…

Q: snip

A:

Q: sin(-æ) = - %3D V2 tan(x) = – %3D cos(x) csc(x) cot(x)

A:

Q: cosx y = x 2 (sin -1 x) 3 y=ー cos X 6. 5.

A:

Q: sin(x+y) Verify that (sec x cos y + sin y csc x) %3D sin(2x)

A: Prove that sin(x+y) /sin2x?

Q: 1. cos x 1 - sin x = sec x + tan x

A:

Q: 40. y = -3 cos x 39. y =-4 cos x 42 y= 41. y

A:

Q: sin(cos y) y 4-lim, 2

A: Limit Solved .

Q: Verify the identity.

A: Given: To prove the given identity thatcos γ1-tan γ+sin…

Q: 5) Period of y= 2 cos x %3D

A:

Q: sin'x cos'xdk 3. X COS

A: It is given that, ∫sin2xcos3x dx We have to solve it.

Q: sin . sin . cos x d. cosz tan E tanz 214 14

A: Given that,

Q: y = Vsin (x)+ /sin(x)+. sin (x)+ sin (x)+ Vsin (x)+

A:

Q: sin x+cos X 4 Jo 9+16sin 2x

A: I = ∫0π4sinx+cosx9+16sin2xdx ⇒I = -∫0π4sinx+cosx-9+16-2sinxcosxdx ⇒I =…

Q: •π * (sin³ x)√1 + cos x dx 2

A:

Q: sin (x) dx (2+3 cus(x))² 3(2+3 cos(x)) с

A:

Q: cos x dx – sin z V1- sin x Determine

A:

Q: cos (x+ y) cos (x-y) cos2 x- sin2 y

A:

Q: stion Three: If y = sin(x) – sin³ (x). show that y' = cos³(x).

A: We will differentiate the function and use the identity : 1 - sin²(x) = cos²(x)

Q: sec x - cos r cos r tanx

A: Given: secx-cosxtanx Identity used: secx=1cosxtanx=sinxcosxsin2x=1-cos2x

Q: Differentiate. y = 3x2 cos x cot x y' = 6x cos (x)cot(x) + 3x2.-sin(x)cot(x)· csc2(x)

A:

Trigonometric Identities

Trigonometry in mathematics deals with the right-angled triangle’s angles and sides. By trigonometric identities, we mean the identities we use whenever we need to express the various trigonometric functions in terms of an equation.

Inverse Trigonometric Functions

Inverse trigonometric functions are the inverse of normal trigonometric functions. Alternatively denoted as cyclometric or arcus functions, these inverse trigonometric functions exist to counter the basic trigonometric functions, such as sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec). When trigonometric ratios are calculated, the angular values can be calculated with the help of the inverse trigonometric functions.