Make the indicated trigonometric substitution in the given algebraic expression and simplify. Assume x²-1, x= sec t

Q: Use the trigonometric substitution to write the algebraic expression as a trigonometric function of…

A: By using the trigonometry substitution

Q: Simplify the expressions below. (a) tan(cos-1 x) (b) sin(tan1 x)

A: Refer to the question.Let a = cos^(-1) x.  That is from the properties of inverse trigonometric,

Q: Which of the following values of satisfy the equation tan 0 = sin 0? 占2

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Q: Given tanθ = - 2, 270° < θ < 360°, find the exact value of the remaining five trigonometric…

A: Given tanθ = - 2, 270° < θ < 360°, We know that  tanθ=PerpendicularBase Since the tanθ is in…

Q: Simplify cos(sinæ).

A: We simplify the given

Q: Rewrite sin 2 cos as an algebraic expression in v. 5

A: Explanation: Given that,                          We know that,                           Use the…

Q: Make the indicated trigonometric substitution in the given algebraic expression and simplify…

A:

Q: Use the given information to determine the remaining five trigonometric values. Rationalize any…

A: Sin X = Perpendicular/Hypotenuse Cosx=1/Secx Tanx=Sinx/Cosx Cotx=1/Tanx Cscx=1/Sinx

Q: Verify the following trigonometric identity. tan(2)csc(x) = sec(x)

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Q: Find the exact value of the expression. cor( an () sin

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Q: Use the definitions of the trig functions in terms of sine and cosine, the Pythagorean identity, and…

A: 1csc(t)-1+1csc(t)+1Addingcsc(t)+1+csc(t)-1(csc(t)-1)(csc(t)+1)=2csc(t)csc2t-1=2csc tcot2t…

Q: Suppose that Ө is in standard position and   is on the terminal side. Find the exact value of a) r…

A: Given Ө is in standard position and   is on the terminal side.

Q: Simplify  1/cos a 1/sin b

A: we know that  1cosθ=secθ1sinθ=cosecθ

Q: Complete the steps by applying trig identities to show that the left hand side of the equation is…

A:

Q: Complete the steps by applying trig identities to show that the left hand side of the equation is…

A:

Q: Write the first expression in terms of the second if the terminal point determined by t is in the…

A: Given: write sin(t)  in terms of the sec(t) where t is in the IV quadrant.

Q: Use the half-angle formulas to simplify the expression. 1- cos(x – 3) 2

A: We know that cos(2t)=cos2t-sin2t=2cos2t-1=1-2sin2t⇒2sin2t=1-cos(2t)⇒sin2t=1-cos2t2

Q: Question in image.

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Q: Find the exact value of tan 3 Write your answer in radians in terms of t. V 3 JT -1 tan 3

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Q: If you are going to evaluate the x²+16 using trigonometric substitution, the answer is =-csc*Ø + C,…

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Q: Begin by rewriting the given expression in terms of sine only. Then, simplify. cos?(x)

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Q: Write the first expression in terms of the second if the terminal point determined by t is in the…

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Q: cos(T+ tan 1 /2x)

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Q: tan(los +1(-)

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Q: Make the indicated trigonometric substitution in the given algebraic expression and simplify. Assume…

A: For first part, Range of sine function is [-1,1] For second part, substitute x=5costheta and…

Q: Find the algebraic expression for the following trigonometric expression tan(arccos 2x + arctan x²)

A: Give expression is tanarccos2x+arctanx2 We have to find the algebraic expression from…

Q: Make the indicated trigonometric substitution in the given algebraic expression and simplify. Assume…

A:

Q: Complete the steps by applying trig identities to show that the left hand side of the equation is…

A: Consider the given trigonometric expression sinx+tanx1+secx

Q: Make the indicated trigonometric substitution in the given algebric expression and simplify. Assume…

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Q: Find the exact expressions for sin θ​, cos θ​, and tan θ.

A:

Q: Write cos 0 in terms of sin 0, for 0 in quadrant III.

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Q: Write the expression in terms of sin and cosine and then simplify to an expression involving a…

A: Given:

Q: Complete the steps by applying trig identities to show that the left hand side of the equation is…

A: LHS=sinx+tanx1+secx=sinx+sinxcosx1+1cosx=sinxcosx+sinxcosx1+cosxcosx=sinx1+cosx1+cosx=sinx=RHS

Q: Completely simplify the following trigonometric expression: tan (t) +1 sec(t)

A: We will simply using the trigonometric formula

Q: Make the indicated trigonometric substitution in the given algebraic expression and simplify complet…

A: Given that,                                                    4 - x2   According to the question,…

Q: Complete the steps by applying trig identities to simplify the expression as much as possible Steps:…

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Q: Write the following in terms of sin 0 and cos 0 and then simplify if possible. sec 0 tan e

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Q: Use the given conditions to find the exact value of the expression. sin(a) = – 13 tan(a) > 0, sin a…

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Q: tan x-sec²x +3=0

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Q: Use the formulas for lowering powers to rewrite the expression in terms of the first power of…

A: The key step to solve this question is use the formula- Cos2x=(1+cos(2x))/2

Q: Rewrite the expression as an equivalent expression that does not contain powers of trigonometric…

A: (i) The given trigonometric expression is

Q: Suppose 0 <m(8)<, and x=2 sec(0). What is the resulting expression if we write √x² - 4 as a…

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Q: simplify by referring to the appropriate triangle or trigonometric identity. tan(cos−1 x)

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Q: Simplify: cos^4 A − sin^4 A

A: In this question, we need to simplify cos4 A -sin4 A.

Q: If x = 9 tano, use trigonometric substitution to write 81 + x 2 as a trigonometric function of 0.…

A: We can obtain trigonometric function for an algebraic expression by applying trigonometric function…

Q: write the expression below in terms of a single trigonometric function  sin(5x) cos(2x) + cos(5x)…

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Q: simplify the equation below to an expression involving a single trigonometric function with no…

A: Solution: The objective is to simplify the given expression

Q: Simplify the following into a Single trigonometric Function. Sec(x) + cotlx)csCLx) seccx)tancx)…

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Q: Make the indicated trigonometric substitution in the given algebraic expression and simplify x = 2…

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.