5 2. If sin 0 = 13 <0

Q: 1- cos 20+ sin 20 Prove tan e. 1+ cos 20+ sin 20

A: We can prove the given statement as below

Q: (-n *) Prove sin? x – sinx cosx – 2 cos? x =0 in п, 2 has five root's Hint. Intermediate value…

A:

Q: 5. Given that 2 sin 20 = cos 20, a) show that tan 20 = 0.5. b) hence find the values of 0, to one…

A: given that 2sin2θ=cos2θ to prove that tan2θ=0.5 proceed as follows  2sin2θcos2θ=1tan2θ=12tan2θ=0.5

Q: 6. Suppose that sin(0) of sin(20). 15 and that the terminal side of 0 is in the second quadrant.…

A: The solution is:

Q: Find the exact value ofcos(α+β)under the given conditions.   sinα=15/17, 0<α<π/2​;…

A:

Q: Prove that: 1-tan? 0 cos? 0 - sin? e %3D 1+tan? 0

A: A function is said to be a rational function if it is given as the ratio of some values.  The…

Q: Show that 2 sin 0 + sin 20 sin 0 1- cos 20 1 cos e Prove that (G) 1 T 1 tan-1 + sin V5 3. where…

A:

Q: B) Prove that: 1-tan? 0 cos? 0 – sin? 0 - 1+tan? 0

A: Such identities can be proved by taking one side of the identity and proving it as equivalent to the…

Q: Which of the following is equivalent to sin 0 tan 0 csc 0 for all values of 0 for which sin 0 tan 0…

A:

Q: 4.1- cos? 0 = sin 0cose tan 0

A:

Q: 1. Prove cos 8-sin 8 cos 8 + sin e = sec 28 tan 20.

A:

Q: (a) i) Prove that 1 sin20 1 tane 1+ sin20 1+ tane for 0<0 <- 4 ii) Hence, show that the exact value…

A:

Q: 12 Prove that sin 80 cos 0-sin 60 cos 30 a. = tan 20 cos 20 cos 0- sin 30 sin 40

A:

Q: B) Prove that: 1-tan? 0 cos? 0 – sin? 0 1+tan? 0

A:

Q: 2 _ 2 if tane + sin0= m and tan0 – sin0 = n ,show that m² – n´ = 4 mn

A:

Q: given that sin(x)=11/61, and 0<x<<x<pi/2 find cos(2x)

A: Given that sinx=1161             0&lt;x&lt;&lt;x&lt;π2 The interval shows that x is in first…

Q: 4. Given that V2 – v2 sin 22.5° find an exact expression for tan 22.5°. 2.

A:

Q: 9. Evaluate. Give the exact answer, not a rounded off decimal. a. tan−1 (√3) b. sec (sin−1 ( 5 13))

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Q: a) By using identity cos(A+B)=cos Acos B-sin Asin B, prove that 4 sec e 3-tan' 0 sedo + 30°)sec(0-…

A:

Q: Part 3 of 4 COS X d —CSC X + С dx To check for the result, prove that 1 - cos?x

A:

Q: If 1, = | x" sin x dx, prove that 1, = nx"-! evaluate -1,. sin x- x" cosx– n(n-1)I, 2. Hence, = NX…

A:

Q: 2. Prove using the angle sum identity of sine: sin 90° = 1.

A: 2- Given- sin90°=1 To prove- The above expression using sum identity of sin. Identity Used-…

Q: B) Prove that: cos? 0 – sin? 0 1-tan? 0 =- 1+tan? 0

A: B)cos2θ-sin2θ=1-tan2θ1+tan2θRHS1-tan2θ1+tan2θ

Q: 15. Find sec0, given that sin 0 2 ,and 0 is in QIII. 5/21 21 d.- а.- 21 21 5 16. Find cos e using…

A: Use trigonometric identity to find value

Q: Prove 3n - T, 2 sin? x – sinx cosx – 2 cos? x=0 in has five root's Hint. Intermediate value theorem

A: Corollary of Intermediate value theorem :- If a continuous function has values of opposite sign…

Q: 24 If tan(0) = 10 0 <0< 90°, then the exact value of Hint sin(0) = %3D cos(0) : COS %3D sec(0) = %3D

A:

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

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

Q: considering only the values of θ for which sec^2θcos(2θ) is defined, sec^2θcos(2θ)= ?

A: SecA=1/cosA Cos2A=2cos2A-1

Q: 8. a. Verify the given identity: sec(0)- cos(0) = sin(0))tan(0) b. Use part a to solve the equation:…

A: (a) given as sec θ- cos θ= sin θ tan θ Simplify left-hand side as sec θ- cos θ= 1cos θ-cos…

Q: 7. Given that sin 0 and 270° < 0 < 360°, sketch 0 in standard position and fir %3D - 13 a. sin b.…

A:

Q: Find sin(2θ), cos(2θ) and tan(2θ), given that sin(θ) = 4/5 and sec(θ) < 0.

A:

Q: Find the exact value of sin 20 if tan 0 with 0 in QII. 4 %3D O - 8 17 13 17 8 17 17 o 4V17 17

A:

Q: 7. Consider the identity _2 tanr 1+tan z sin(2r). (a) Verify the identity. (b) Find sin (4) if tan…

A:

Q: find exact value 197 8. (a) cos 6 (b) сos 6 (c) cos 6 9. (a) cos 4 (b) cos 4 (c) cos 4 10. (a) sin 4…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 1. If theta = arcsin(1/2) and 90deg < theta < 270deg, what is tan theta? 2. Find the value of…

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Q: (a) Use the identity cos'0 + sin 0 = 1 to prove that tanʼ0 = sec² 0 – 1

A:

Q: 7. Verify the identity 1+cos 2x+2sin² x = 2 1 and <θ<π, find sin- 8. Given tan O 3 2 9. Use half…

A: Explained below

Q: Express as a sum or difference:4 sin 3 θ cos 7 θ

A: Consider the provided expression, 4sin3θcos7θ Express as a sum or difference. Use the formula of…

Q: 1. By considering (1+ expi®)", prove that "C, cos r0 = 2" cos"(0/2) cos(n /2) (ii) ►"C, sin r® = 2"…

A: First, expand the given complex function:

Q: 7) Find the value of 0 degrees rounded to 2 places, given: sin 0 = -.7568, tan 0 < 0

A: Important points for the question: tan θ &lt; 0  =&gt; tan θ = negative tan θ = sin θ/cos θ   sin θ…

Q: Find the smallest possible solution to the equation 7 tan(4a + 199°) = 8 sin(4a + 199°), where a >…

A:

Q: what is the exact value using half angles for 1. sin(11pi/12) 2. cos (7pi/8) 3. tan (5pi/12

A:

Q: 9 Suppose that a cos x = 1 + sin x, where 0° < x < 90°. a a Prove that 1 = t, where t = tan x. a + 1…

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Q: Q1- Show that cote)+tan(e) a. cofe)-tan(9) sec(20) b. sin(36) = 3 sin(@) - 4sin (0) = Se %3D

A:

Q: Suppose that π/2≤θ≤π, sin(θ)=2/10, find tan(θ)=______. (round to 3 decimal places)

A: Given:-sinθ=210π/2≤θ≤π

Q: Given that sinθ= 3/5 and cos(θ)<0 that , what is the exact value of sec(θ)

A:

Q: cos 30° + sin 60° V3 Prove that 1+ cos 60° + sin 30°

A: Trignometric ratios are

Q: Suppose, for some angle 0 drawn in standard position, tan(e) = -24/7 and sin(0) < 0. Find the exact…

A:

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.