Verify that the following expression is an identity by simplifying one side of the equation to equal the other side. cot(x) + tan(x) = sec(x) csc(x)

Q: Write the given expression as an algebraic expression in x. cos(2 tan-1 x)

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Q: Simplify the following expression to a single trig function: cos(5æ) cos(2a) + sin(5æ) sin(2æ).

A: Given : cos5xcos2x+sin5xsin2x

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: Verify the identity.

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Q: sin(A) tan(A)+ cos(A) = COS

A: Given- sinAtanA+cosA To Simplify- The above trigonometric expression. Identity Used- sin2A+cos2A=1.…

Q: Prove that each equation is an identity. sin 20 (b) 1+ cos 20 = tan e sin (s-t), cos (s -t)_ sin s…

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Q: 1. Explain the steps in verifying that the following equation is an identity. cos x sec x + tan x =…

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Q: Write the given expression as an algebraic expression in x. sin(2 tan-'(x))

A: Trigonometric

Q: Write the given expression as an algebraic expression in x. tan(2 cos-1(x))

A: According to the question, we have to solve the expression tan2 cos-1x and write as an algebraic…

Q: Verify that each equation is an identity 1. sin 4x = 4 sin x cos x cos 2a

A: To verify:

Q: Simplify the identity, show all steps. sin(x) 1+cos(x) 1. 1+ cos(x) sin(x)

A: We use identities  sin2(x) +cos2(x) = 1  1/sin(x) = csc(x)

Q: Verify the following identity. 2 sin x+ cos 2x = 1- sin x

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Q: Use the fundamental identities to fully simplify the expression. sin(x) cos(x) csc(x)

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Q: Given the expression below, determine tan (0/2). sin 0 - x². 1+cos 0

A: We have to find the value of tanθ2 by the given expression sinθ1+cosθ=x2 first using the formula of…

Q: Rewrite the following expression in terms of the given functions. 1 cos x and sin x tan X+ cot x

A: We have to Express

Q: Verify the identity. (Simplify at each step.) (1 + sin a)(1 – sin a) = cos? (1 + sin a)(1 - sin a) =…

A: Simplification

Q: Verify that the equation is an identity. 41) cos 즉 2 = 1 - sin x 2 X sin 2

A: Here we have to verify the equation is an identity.   [cos(x/2) - sin(x/2)]2 = 1 - sin x

Q: In a brief, substansive, grammatically correct statement, describe the first step you are inclined…

A: In a brief, substansive, grammatically correct statement, describe the first step you are inclined…

Q: Prove the following identities by choosing one side and manipulate until you arrive at the other…

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Evaluate the following expression. tan(sin^-1(x))

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

A: To prove:

Q: Verify the following identity. -2 tan e sin 20 = 2. 1+ tan 0

A: Here I am attaching image so that you understand each and every step.

Q: Verify the following identity. sin x+ cos 2x = cos To transform the left side into the right side,…

A: Trigonometric identities are mathematical equations that stay valid for right-angled triangles.…

Q: Verify the identity by following the steps below. sin(x)cot(x) cos(x) 1) Write the left-hand side in…

A: To verify the identity sinxcotx=cosx.

Q: |Verify the following identities by converting the left side into the right side step-by-step. Write…

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

A:

Q: Prove the following identity. (sin x – cos x)2 = 1 - sin 2x We begin by expanding the left side of…

A: Given : sinx - cosx2 = 1 - sin2x

Q: Prove that the following identity is true. 1 1 = 2 csc? x 1 + cos X 1- cos X We begin on the left…

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Q: Show that the following statement is an identity by transforming the left side into the right side.…

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Q: b. In cot(x)- In | tan(x)| = 2 1n| cot(x)|

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

A: (a)

Q: Write the given expression as an algebraic expression. sin(arcsin x + arccos x) 2 1- x* + X 2 + 1 1-…

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Q: Find the identical expression for the following. cos(x+ )+ cos(x- O cos x O - cos x O - sin x 00 O…

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Q: Simplify the following expression by first substituting values from the table of exact w resulting…

A: Given: 2 cos 60o

Q: If the identity sin (x + a) = sin x cos a + cos x sin a is differentiated with respect to x, is the…

A: The equation is differentiated with respect to x. a is constant with respect to x.

Q: tan x + cot x = sec x CS z

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Q: Write the given expression as an algebraic expression in x. sin(2 tan-¹(x)) X

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Q: Establish the following identity: tan?x – sin?x = tan?x · sin?x

A: Explanation of the answer is as follows

Q: Simplify the following expression in terms of x. (tan (2x)+ cos "(x)] Cos + COS

A: To solve the expression in terms of x

Q: Use a counter-example to show that the following equation is NOT an identity. sin(x + y) = sin x +…

A: Trigonometry function 3π/2=270° π=180° π/2=90°

Q: Write the given expression as an algebraic expression in x cos(2 tan−1(x))

A: Given:

Q: Verify that the equation is an identity. 2 tan 1+ cos x

A: we know thatcosx=2cos2x2-1consider…

Q: Simplify the following expressions. sec x-cOS X 1. sin x

A: The given trigonometric equation is: sec x-cos xsin x

Q: Verify the identity by following the steps below. sin(x)cot(x) cos(x) 1) Write the left-hand side in…

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Q: If cp (x) =cos x, find e (-x)

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Q: Write the given expression as an algebraic expression in x. tan(2 sin-1(x))

A: To solve the following problem

Q: Use an appropriate identity to find the exact value of the expression. sin (165°) -N2Wa+1) 4

A: Consider the given expression: sin (165°)

Q: 1- sin(x)cos(x) sec(x) – sin(x): cos(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.