estion 46 of 60 What are all values of x in the interval 0, for hich (tan x)(2 sin x 1) = 0 ? - Pre 0. 3. 0,

Q: Prove the identity. 10 10 + = 20 sec %3D 1- sin x 1+ sin x

A: Take lcm and then solve

Q: (A) Verify the identity (i) (1 + tan² x)(1 - sin2x) = 1 sec x - 1 %3D tan x (ii) tan x sec x + 1 1+…

A: We have to prove the identities.

Q: 10. Prove the following identity: tan² x+1 1 %3D tan² x-1 sin² x-cos² x

A: Topic - trigonometry

Q: 5- Prove that a) tan x (csc x – sin x) = cos x b) 1+ sec?x sin?x = sec?x

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Q: Which of the following is equivalent to secβ(tan2β+1) for all values of β for which secβ(tan2β+1) is…

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Q: -3t Compute the exact value of tan -3T tan 8.

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Q: .2 -If tan -1 = 0, then prove that x2 sin 2 a. %3D

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Q: A. PROVE THE FOLLOWING IDENTITIES: 3. tan*x + tan²x = sec*x – sec'x tanx+secr-1 1+sinx tanx-secr1…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: -1 3. Show that sin-¹x = tan X √1-x² if |x| < 1.

A: Introduction: When there are trigonometric functions present in an expression or equation,…

Q: Prove the identity. 3 sin(x - y) 3 tan x - 3 tan y = cos y cos x

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Q: Find all values of x in the interval [0, 27] that satisfy the equation. (Enter your answers as a…

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Q: Prove the identities. 2 tan x (a) tan 0 sin 0 + cos 0 = sec 0 (b) 1 + tan?x sin 2x

A: To Determine: prove the identities  Given: we have  tanθ sinθ+cosθ=secθ Explanation: we have an…

Q: 2-tana 11. If Sin(x+ a) = 2Cos(x - a); prove that : tan x = 1- 2 tan a

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Q: 2. What is the exact value of tan (-75°)? O 2-V3 O-2+ V3 O 2+ v3 O-2-V3

A: To find :  The exact value of tan(-75°). Note: To find the exact value apply the reference angle by…

Q: 04) Prove that 1- Cos + x) = sin x, 2- (sin x +cos x) sec x = sec2 x %3D

A: We have to prove that following trigonometric identity.

Q: Lan: prove (:) - - 4. sin x tan =1- cos x

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

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Q: 48. tan x = -0,974; con 5 < x < a a. sen x d. sec x b. cos x e. csc x) c. cot x

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Q: 10. Prove the identity: 2 + cot² (x) _ 1 = sin² x - csc² (x)

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Q: Which of the following is equal to tan(T – 0)? sin(0) O cos(0) O sec(0) O csc(0) tan(8) cot(8) -…

A: Just I have used the trigonometrical formulas and identity and get the required solutions.Solutions…

Q: Prove the identity 1/Cos X - 1/Sec X = Tan X * Sin X

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Q: In Exercis express the given quantity in terms of sin x and cos x.

A: Here we have to express cos(π+x) in terms of sin x and cos x.

Q: Verify the identity (1 + csc x)/sec x - cot x = cos x

A: We have to verify: 1+cosecxsecx-cotx=cosx We will use following relations of trigonometric…

Q: (-등, 풍) satisfying TT Find all values of 0 in the interval 2 2 2 the equation (1 – tan 0)(1 + tan 0)…

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Q: 1 Verify the identity 1 = 2 tan x sec x %3D 1-sin x 1+sin x

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Q: 2- tana 1. If Sin(x+ a)= 2Cos(x-a); prove that: tan x = 1-2 tana 2 If Siu

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Q: Prove the identity cot x- tan x = 2 cot 2x

A: Since you have posted multiple questions, we will answer the second question. If you want the…

Q: Q Prove the following identities 1-sin (1) sec-tan ) 1 sin

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Q: 2. Verify the following identities (a) sec e - tan@ =sec 0+tan6 sec 8+tan 6

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Q: 8. Find all 0 such that -180° <0 < 180° and: cos 0 = - b sin 0 = c tan0 = - a d cos 0 = 0.8 e tan 0…

A: we have given -1800≤θ≤1800a. cosθ=-110⇒θ=cos-1(-110)=95.740b. sinθ=45⇒θ=sin-1(45)=53.130c.…

Q: 4.) Prove: sin 2x a) 2cos? x = tan x b) sin 3x = 3 sin x – 4sin3 x [Hint: sin 3x = sin(2x + x)] -

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Q: 8. Prove that tan? 0 + cos? 0 + sin² 0 = sec² 0. %3D

A: Explanation and solutions is given below....

Q: 13. Write sin(tan-)) ; x > 0, as an algebraic expression of r. 49 + x² iv) 7 ii) 49 + x² iii) 49 +…

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Q: Suppose you know that sin x ≈ 0.35 and cos x ≈0.9. What is then ( look at the picture)

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Q: Find all values of x in the interval [0,360) that satisfy the equation. Use degree measure.…

A: Given

Q: 1) Prove that cose-sin*e 1- tan?e cose

A: Trigonometric identities help to prove the required expression. The algebraic formula…

Q: The Function f(x) = sin( 2")- sin( 2 *) is %3D Select one: O An even Function O An odd Function O…

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Q: Prove one of the following identities. 1-tan2 x 2 tan x Cos 2x = sin 2x 1+tan2 x 1+tan² x

A: Please check step 2 for the solution.

Q: Prove the identity. sin2(x)−tan(x)/cos2(x)−cot(x)=tan2(x)

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Q: Prove the identity. sin(n-x)сos(n+x)tan(2π − x) T 3π 3π sec+ x)csc(³7-x)cot (³7 + x) = sin^x - sin²x

A: I have appended the formula used in the solution part of the question

Q: 7. Verify the identities: tan x tan x tan20 1-cos e a) 1+sec x = 2 csc x b) sec 0+1 %D 1-sec x cos e

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Q: 5.) Prove the identity. cot(x) + tan(x) = sec(x)csc(x)

A: To prove that  cotx + tanx = secx.cosecx

Q: Prove: 1 + 1 = 2 sec? x 1-sin x 1+sin x

A: Prove   1/(1-sinx) + 1/(1+sinx) = 2sec2x

Q: Derive the formula for Sin(A-B) (Hint: use formula Sin(A+B) and even/odd functions

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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: a. Show that y = tan u increases on every open interval in its domain. b. If the conclusion in part…

A: (a)  Given,

Q: Verify the identity. 1+ sin(x) = (tan(x) + sec(x))² 1+ sin(x) 1 - sin(x) 1- sin(x) 1+ sin(x). 1 +…

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Q: Prove the identity. 4(tan(x) – cot(x)) tan2(x) – cot2(x) | = 2 sin(2x) %3D

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

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.