(a) Show that tan? 0 = } if and only if sin? 0 = 1/4. %3D (b) Use part (a) to find all the values of 0, –T

Q: 3. Find the exact value of the expression: sin tan-1 12 [tan- + cos

A: We have to find

Q: 12. Verify the identity by transforming the left side of the equation into the right side. csc 0-sin…

A: 12. We need to verify the following identity cscθ-sinθ = cotθcosθ

Q: 8. Find the values of the six trigonometric functions of 0, if tane = 2 and sine < 0. sine = csce =…

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Q: Find the exact value. a. sin ( tan-1 24. cos (sin-1 (-) T c. cos(tan-1 2) | OS

A: We can find the answer as below.

Q: Express sin 0 cot in terms of first degree sine or cosine function. sin 0 (1+ cos 0) O sin 0 (cos 0…

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Q: 1 cose cote+ + -is equal to tan e sine 3 sin 0 3 cot 0 3 cot 3 tan 0 3 cos e

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Q: Evaluate in degrees without using a calculator.      a. sin−1(1/2) = °      b. cos−1(1/2) = °…

A: Topic  = Trigonometric ratios As per guidelines  , At a time only three sub-parts of a question can…

Q: Find sin 0 and tan 0. cos e = sine = tane

A: Given :               cos θ = 25Then hypotenuse = 5 , adjacent = 2 and opposite = ?   To find the…

Q: 8 and sin(0) > 0, then find 7 If tan(0) (a) sin(0) (b) cos(0) || (c) sec(0) (d) csc(0) (e) cot(0) =…

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Q: Prove the identity. sin(x -) - -cos(x) Use the Subtraction Formula for Sine, and then simplify.…

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Q: 3. Evaluate and solve for x. (No decimal values allowed) tan 30° sec60°sin90° esc-45 sec600 X(sin…

A: Put tan30°=1/√3, sin30°=1/2, sin90°=1 Cosec45°=√2, cos45°=1/√2 Then solve for x

Q: Cos e sin 0 sin 0 + cos 60 (1 - tan 0) (1- cot 0)

A: cosθ1-tanθ+sinθ1-cotθ=cosθ1-sinθcosθ+sinθ1-cosθsinθ=cos2θcosθ-sinθ+sin2θsinθ-cosθ=cos2θcosθ-sinθ-sin…

Q: 6 what is sin(-x)? 7 Given that sin(x) Provide your answer below: sin ( – x) =

A: Given  Sin(x)=6/7 Sin(-x)=?

Q: Find the exact values of the trigonometric functions. (1) Given sinθ = −4/11 and tanθ > 0, , find…

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Q: Determine a root of the equation sin x + 3 cos x – 2 = 0. Correct to four decimal places

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Q: owing is equivalent to sin (-0)cos Ocsc (-0)sec (-0) for all values of 0 for which c(-0)sec (-0) is…

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Q: 8 If tan 0 15 what is sin 0? sin 0 = [?] %3D

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Q: 5. Establish the identity: tan 0 +cot 0 = sec 0 csc LHS COSE Sine Sude

A: consider the given identities

Q: (cor- (-꼴)) + tan-1 (sin (5)) ? What is the exact value of sin COS 2 -2/2-T 4 -2/2+T 4 2/2+T 4 2/2-n…

A: We have to find the value of the given condition

Q: 3 TC Suppose that sin 0 = and <0<n. - Find the exact values of cos and tan 2 - 2

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Q: cos 0 tan 0 + sin 0 Express as a single trigonometric function of 0. cos 0

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Q: 7. Solve the trigonometric equation exactly on 0= tan?0+tan@ =0

A: tan2θ+tanθ=0tanθ(tanθ+1)=0tanθ=0 , tanθ=-1 For tanθ=0 tanθ=tan0θ=0 For tanθ=-1 tanθ=tan135θ=135

Q: Determine the values of the trigonometric functions of 0, where sin 0 = and cos 0> 0. 13 cos 0 =…

A: Given query is to find the value of 6 trigonometric functions.

Q: 2.a. If cot(0) = and sin(0) < 0, find all six trigonometric function 45 values for 0.

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Q: Use fundamental identities to find the values of the trigonometric functions for the given…

A: Given, tanθ=-34  and  sin θ&gt;0

Q: Prove the identity. sin(x - ) - -cos(*) Use the Subtraction Formula for Sine, and then simplify. sin…

A: Given that, sinx - π2=-cosx We have to prove this identity. We know that, The substraction formula…

Q: 46. What are the advantages to using the formula a_1- cosa tan 2 sina or tan as opposed to sina 1 +…

A: To obtain the formula for the tan half-angle, write tan x as sin xcos x and then substitute the…

Q: If sinx = 1/√5 and cosx < 0, find sin(2x)

A: Given : If sinx = 1/√5 and cosx&lt;0,   Now,                sin2x = 2 sinx cosx        ....(1)…

Q: 2. Find the values of other trigonometric identities if sin 0 3 and tan 0 > 0.

A: Explanation of the answer is as follows

Q: -1 If cot (sin-¹ √√1-x²) = sin (tan¯'(x√6)), x ±0 then the value of x is.......

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Q: Find the EXACT value of sin ø, and cos ø if tan ø = -3/4, cos X < 0

A:

Q: 5. If 0° < 0 < 90° and tan 0 =, find sin 0 using trigonometric identities. 3/5

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Q: Use fundamental identities to find the values of the trigonometric functions for the given…

A: Given that, cosθ=-13 and sinθ&lt;0 Since in the third quadrant both sine and cosine are negative.…

Q: Express sin()cos()+cos() sin() as a single trigonometric ratio. a) sin(2x) Ob) cos(x) Oc) cos(2x) O…

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Q: Find the values of the trigonometric functions of 0 from the information given. tan(0) -3, sin(0) >…

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Q: sin x cos x # 0, What is cot x =? COS X If tan x =

A:

Q: Prove that the equation is an identity. 1 - sin 0 = cot 0 cos 0 sin 0 Working from the left-hand…

A: Using 1-sin2 x=cos2 x

Q: 4 -- and sin 0 < 0, find the values of the other 3 trigonometric functions of 0.

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Q: Find sin 2 and tan from the given information. 2 CoS 2. sin(x) = 25 0° < x < 90° sin(즐)- 2 Cos 2…

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Q: (b) Show that sin50=(Q sine-R sin 30+S sin 50 ) by using De Moivre's Theorem. Hence, state the…

A: We have to express sin5θ   in the form   sin5θ = 1PQsinθ-Rsin3θ+Ssin5θ using De Moivre's Theorem. At…

Q: 2) Find the values of the six trigonometric functions for 0. Ar 5 12 sin 0 = csc 0 = cos 0 = sec 0 =…

A:

Q: 37 and :, =4 cos 18 cos +i sin +i sin pllowing. answers in trigonometric form. = values in your…

A: We have to find the given expression from the given information

Q: 5 and tan e <0. 8 2. Find the values of all trigonometric functions of e given that sin e = - Give…

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Q: sin(ø) = 2 3 and <0. Given that <0< what is the exact value of cos(20)?

A: Here, given that sin θ=23; π2&lt;θ&lt;π That is θ is in the second quadrant. Therefore, cos…

Q: sin(2x)/1 +cos(2x) verify the trigonometric identity

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Q: tan 0 4. Given sin 0 %3D 4 and > 0, find other trigonometric functions?

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Q: If tan 0 = 10 - sec 0 with 0 in quadrant I, what is sin 0 + cos 0? sin 0 + cos 0= (Type an integer…

A: Given is a relation for angle theta in first quadrant. First we substitute tan(a)=sin(a)/cos(a),…

Q: Simplify. sin(-0) tan(-0) sec(e) cos 0 o -sin?0 -cos20 COsS sin 0

A:

Q: What are the values of 0 between 0 and 2T (inclusive of 0 and 21) that satisfy the trigonometric…

A:

Q: 8. If tan 0 = 15 what is sin 0? sin 0 = %3D iblo

A: The solution is given below in the next step:

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.