By using the relationship between the hyperbolic sine function and its Ssinh- (x)] = V. inverse, prove VI+x?

Q: State the half-angle identities used to integrate sin2 x and cos2 x.

A: Given, The functions are sin2 x and cos2 x

Q: Evaluate∫cos 6x dx without using the substitution method.

A:

Q: Express sin S as a fraction in simplest terms.

A: Topic:- trigonometry and geometry

Q: . Give the exact value of sin V3 2.

A: Given: sin-132

Q: (1) / in | (sin-x)° dr

A:

Q: Reduce sin 0 to an expression involving only function of multiples of 0, raised to the first power.

A: Given, sin4θ  We have to reduce sin4θ to an expression involving only function of multiples of θ,…

Q: COSX 1+sin2x

A: Solution: The objective is to find the solution to the given differential equation.

Q: find the value of cE CoB] for flx)= that satisfy value theorem. mean

A:

Q: What is the value of sin(2x + 3)dx?

A:

Q: Express sin 5x cos 3x as a sum of trigonometric functions.

A: Given           sin 5x cos 3x

Q: The suitable substitution to evaluate sin24(x + 2) dx is

A: Proceed as shown below...

Q: Use a trigonometric identity to show that the derivatives of the inverse cotangent and inverse…

A: To show: The derivatives of the inverse cotangent and inverse cosecant differ from the derivatives…

Q: sin 2tan

A:

Q: State the half-angle identities used to integrate sin x and cos x.

A: Half Angle Identities are the formulae/relationships used in trigonometric functions to reduce the…

Q: = 4 cos 3x – 3 sin 4x

A:

Q: Use the definition of the hyperbolic sine to show that sinh x is an odd function.

A:

Q: Solve Sin (3x) %3D cos (2x)

A: to find derivative of y=sin3xcos2x

Q: In the given question, verify the identity:-   sinh 2x = 2 sinh x cosh x

A: To prove  sinh2x=2sinhxcoshx.

Q: Since the functions y cos(x) and y -1 = cos are inverse functions, explain why COS (cos(-)) is not…

A: use the range of arc cosx to find the values

Q: 2. Is trigonometric substitution needed to evaluate /9 - x² dx?

A:

Q: Find an equivalent expression for sin 4x in terms of function values x sin 4x =

A: power series of f(x) about x =a is  f(x) = ∑h=0∞ fn(a)n! (x-a)n ------- (*)

Q: If x = 8 sec 0, express tan e in terms of a. %3D

A: Given: x=8secθ Express: tanθ in terms of x

Q: Why are different intervals used when restricting the domains of the sine and cosine functions in…

A: Why are different intervals used when restricting the domains ofthe sine and cosine functions in the…

Q: The simplified form of [csc(-x) + cos(-x)] · [9 sin² æ sec? æ]

A: The simplified form of [csc(-x) + cos(-x)] [9 sin²x sec² x]

Q: Evaluate 2 sin² x cos³ x dx 0,

A: Given that: ∫0π2sin2x.cos3xdx

Q: For y=2sin(9x)y=2sin(9x), its amplitude is__________ its period is __________

A: Given that y=2sin(9x) To find Amplitude and period.

Q: Evaluate [si sin 3x cos 5x dx.

A:

Q: Find a value of x that satisfies the equation sin 53° = cos (x). %3D

A:

Q: Estimate sin 61◦ − sin 60◦ using the Linear Approximation. Hint: Express∆θ in radians.

A: Consider the given trigonometric expression sin61°-sin60° Suppose the linear approximation for the…

Q: Why is cos(sin^-1(x)) equal to sqrt(1-x^2)?

A:

Q: Express sin 0 cos 0 in terms of a if cot 0 = a

A:

Q: Find a value of x that satisfies the equation sin (-84°) = cos (x). %3D

A: To find: The value of x. Given: The equation sin-84°=cos x. Concept used: sin-θ=-sin θ sin3π2-x=-cos…

Q: 4. Find the exact value of sin if cose 2 3 and e is in QIII. cose =-- |

A: According to question,Given conditions,cos θ = -35,θ is in third quadrant.

Q: Find the exact value. -5n sin- 6. Type + or - [ ?

A:

Q: The value of cos(arctan(x) ) is equal to

A: 1. Given expression, cos(arctan(x))

Q: /2 sin-1 (-)

A:

Q: The x2-4 dx can only be evaluated using trigonometric substitution technique. A True False

A:

Q: Find S(-sin³0 – sin@cos20)d0

A: This can be solved as follows:

Q: Prove that csc2A tan(2A) = 2cosA/cos(2A)sinA

A:

Q: sinx In (2) cos:

A:

Q: A ladder 12 m long rests against a vertical wall. Let theta be the angle between the top of the…

A:

Q: To evaluate sin42x cos 2x dx , the identities to be used is/are: sin4x, 1+ cos4x &- 2 (А) (B) cos?2x…

A:

Q: if sinx=1/8 and x is in quadrent 1, then cos(180-x)=???

A: Simplify cos(180-x),

Q: To approximate the value of sin44° , we will use y=sinx. What must be the yalue of dy ?

A: the aproximate value of sin44 = 0.6946 for approximation  let  y= sinx dy = cosx(dx)             x=…

Q: Evaluate: cos x-sin(sin x)dx and explain your answer in terms of odd/even functions.

A:

Q: Evaluate ∫sin3 x dx by splitting off a factor of sin x, rewriting sin2 x in terms of cos x, and…

A: the given integral is: ∫sin3x dx we have to evaluate the given integral by splitting off a factor of…

Q: State the period length of the function f(x) = -4 sin (27x).

A:

Q: Find sin 0 and tan 0 if the terminal side of 0 lies along the line y = -7x in QII. sin 0 = tan 0:

A: Given that terminal side of ϑ lies along the line y = -7x. Note that the slope of the line y = -7x…