write the following in terms of x without trig or inverse trig functions and simplify. In each case, assume x has a value that makes the expression well-defined. Show steps: sec(tan^-1  x/2)

Q: Use a calculator to compute sinhx and coshx for x = -3, 0, 5.

A: We use a calculator to find the values.

Q: please show all steps to verify a identity  (1/1+sinx)    -    (1/1-sinx)  =-2sinxsec2x

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Q: Express the difference sin x - sin 2x as a product. If possible, find this product’s exact value.

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Q: Simplify the express: sec(tanx).

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Q: (1) / in | (sin-x)° dr

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Q: Which expression is equal to (icnx - 1)/(tan x + 1) using identities ?

A: The given question is taken from the tringnometry in which we have to find the equalent form of the…

Q: Find the exact value of the expression whenever it is defined.

A: Definition used -                       Domain of sin-1(x) is [-1,1].                       Range of…

Q: If x > 0, write sec(tan-1 x) as an algebraic expression in x.

A: Now let

Q: tan(t) Simplify sec(t) – cos(t) to a single trig function.

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Q: Express the product sin 6x sin 4x as a sum or difference.

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Q: Simplify to a single trig function with no denominator. tan O* cos O O sin O Cos O O tan O Csc O

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Q: Use a calculator to solve the equation tan x = -5, correct to four decimal places, on the interval…

A: the given equation is tanx=-5. we have to find the solution of the given equation on the interval…

Q: Evaluate without using a calculator. sin−1(−1)

A: We have to evaluate: sin-1-1

Q: If f(x) =tan(3x) find f'(4)=?

A: Differentiating with respect to x, we get

Q: Simplify sin x (1-cosx)(1+cosx)

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Q: express as an algebraic expression in terms of x. sin(arctan(x))

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Q: Verify each identify and show the process. sin 2x = 2 tan x 1- sin2 x

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Q: Simplify sec(pi/2 -x)to a single trig function using a sum or difference of angles identity

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Q: Evaluate tan (7x+1) sec³(7x+1) dx .

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Q: Write 9 sinh(x) + 4 cosh(x) in terms of e* and e*. +

A: Answer is given below...

Q: Verify that the equation is an identity. cos 2x = COS X - Sin x tan x CoS X To verify the identity,…

A: Using trigonometric formula, we verify

Q: simplify sin2x +cos 2x for x =30

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Q: If  f(x)=sin3x, find f'(x)   find f'(2)

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Q: 6. sin(tan¬1 x)

A: Use inverse trigonometric method

Q: 3. sec-1 -tan

A: Given,

Q: Verify the identity. (Simplify at each step.) sin 5/2 X cos x - sin/2 x cos x = cos xV sin5 x A

A:

Q: If x = 4 tan θ, express sin θ in terms of x.

A: Given that: x=4tanθ To solve the given trigonometric function,…

Q: Simplify the expression to one term. Graph the original function and your simplified version to…

A: Given: sin(x)cos(13x)-cos(x)sin(13x)

Q: Which expression is equivalent to sinβcscβsecβ for all values of β for which sinβcscβsecβ is…

A: According to reciprocal identity csc x=1sin x

Q: Use inverse functions where needed to find all solutions of the equation in the interval [0, 27).…

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Q: differentiate y = sin^3(tet^2) and simplify

A: The given function is y=sin3tet2We have to differentiate with respect to t…

Q: /2 sin-1 (-)

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Q: Express cos4t in terms of values of the cosine function with exponent 1

A: Given,         cos4t

Q: Differentiate sin√(x/x+8).

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Q: Differentiate sin3 x

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Q: Iff = 0.8, simplify the expression tan (tan-(f).

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Q: 1. Simplify tan(x) sec(x) to a single trig function.

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Q: sin2xsec'x = 2tanx %3D

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Q: Use a calculator to solve the equation tan x = -3, correct to four decimal places, on the interval…

A: Given- tanx=-3 To find- The solution of the above trigonometric expression correct to four decimal…

Q: Verify the identity. (Simplify at each step.) 177 sin + X cos(x)

A: Given sin17π2+x=cosx

Q: Evaluate | tan (5x +1) sec³(5x+1) dx

A: We will start with the substitution, cos(5x+1) = t  And proceed as follows :

Q: Use a right triangle to write csc(arccos(3*x/2)) as an expression of x that does not involve trig or…

A: Given:The expression csc(arccos(3x/2))

Q: Write sec x in terms of sin x.

A: Using reciprocal identity we know sec x = 1/cos x

Q: Evaluate tan (8x) sec*(8x) dx.

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Q: tan(sin'x) is ... The simplify of

A: Given expression is Let us suppose Now, Therefore,

Q: Use the addition formulas to derive: cos (x -) = sinx

A: The given equation is cosx-π2=sinx

Q: tan(t) Simplify to a single trig function with no fractions. sec(t) — сos(€)

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Q: Write 9 sinh(x) + 4 cosh(x) in terms of e and e

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Q: By using the addition formula derive the identity of the function sin (x -), then choose the correct…

A: Addition formula for sin is…

Q: Evaluate THT Sin 2X

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.