Prove the following trigonometricidentity: 1 +. sin 6 tan 8 + cos 8 tan 8

Q: Express in the form a + bi where a and b are real numbers.

A: Here given equation is cos 2π/3 + i sin 2π/3 = cos 60° + i sin 60° = 1/2 + i 3/2

Q: Verify the following identity. 1+ cos 2x cotx%D sin 2x

A: Recall: sin2x = 2 sinx cosx cos2x = 2cos2x -1 cotx = cosxsinx

Q: Express in the form a + bi where a and b are real numbers.

A:

Q: Is the following indentity true? cos (0) 1+ sin(@) 1+ sin() cos(0) 2sec(0) COS

A:

Q: solve the following trigonometric equation on [0,2pi): sin(2theta) = cos(theta)

A: To solve the trigonometric equation

Q: Prove the following identity: sin 24 cot A 1-cos 24

A:

Q: Prove each of the following trigonometric identities. 1 + tano : 1+ sin& coso coso

A:

Q: Use the exact values from show thatthe following are true.   cos 2 theta 30 0   + sin 2 30 0 =1 cos…

A: The values you will use : cos30∘=32sin30∘=12cos45∘=12sin45∘=12

Q: To further justify the Cofunction Theorem introduced in theprevious section, use a calculator to…

A: Evaluate: sin(24.3∘) and cos(65.7∘) The given pair sin(24.3∘) and cos(65.7∘) is cofunction of one…

Q: Express in the form a + bi where a and b are real numbers.

A: we have z = 12cos4π3+ isin4π3    Now 4π3= π+π3 hence z = 12cosπ+π3+ isinπ+π3               =…

Q: Prove the following trigonometric identities. 1 cotx a) 6 cosx| 6 cosx = 6sin² x COSX CSCX

A: The details solution is given below

Q: tan 6a sec 3a = 2 sin 3a sec 6a Proof:

A: giventan(6a)sec(3a)=2sin(3a)sec(6a)consider L.H.S.=tan(6a)sec(3a)we know…

Q: b. cos x = -1 y sen « = 0

A: According to the company guidelines only first three subparts can be answered at a time. Kindly…

Q: Prove ONE ONLY of the following identities: Either: tan e + cot e = csc e sece Or: 1+ cos 20 = cot 0…

A:

Q: Find the following special values: sin 0 (5) cos sin 6 (6) sin 3 COS (7) sin 7 sin - (8) (27) cos ||…

A: These angles are all standard angles and hence referring to the table of trigonometric ratios all…

Q: Use trigonometric substitution to compute do o 1+ sin? 0*

A: Final answer is π/sqrt(2).

Q: CSc 0+1 1+sin 6 %3D csc0-1 1-sin 0

A:

Q: If ß is such that sin 230, the of the following two values?

A:

Q: State whether the following statement is true or false. sin20 = 1- cos 20 Choose the correct answer…

A: We have to check

Q: Show that each of the following statements is true by transforming the left side of each oneinto the…

A:

Q: Evaluate the following in trigonometric form: (1-i)* A 16 (cos 2,520 + i sin 2520) B 16(cos 315 + i…

A:

Q: Prove the following identity:  1) sinθ cotθ = cosθ

A:

Q: Find the exact value of cos a/2 given that tan a = 15/8 ,a lies in Quad III.

A: Given: tan a=158 a is lies in Quadrant III. We have to find the exact value of cosa2 Use the…

Q: Verify the following identity: sin 20 – tan 0 tan 0 cos 20

A: To verify the identity: sin 2θ-tan θ=tan θ cos 2θ

Q: Verify the following identities. 1 (1- cose)(1+ cos 0)= csc? 0 2 а. sine(tane + cote)= sec e b.

A:

Q: Show that cos (90 degree - A) = sin A.

A: The given identity is cos90∘ -A=sinA.

Q: sin 4t-sin 2t tan t cos4t-cos 2t 5.

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

Q: Verify the following identities: sin 20 – tan 0 tan 0 cos 20

A: Solved below

Q: Use the given information tan α = 8/15, 180° < α < 270° to find the exact value of the…

A: Use the given information tan α = 8/15, 180° < α < 270° to find the exact value of the…

Q: NTS: COS X sin x Cos 3x sec 2x CSc 2x

A:

Q: Use de Moivre's Theorem to test the correctness of the following trigonometric identity: 3 sin 20…

A: Consider the given trigonometric identity, sin3θcos3θ=3sin2θ-sin6θ32 Here we need to use De Moivre's…

Q: Prove the following identity. sin 20 cot 0 = 1 - cos 20

A: givencotθ=sin2θ1-cos2θwe know double angle formulasin2θ=2sinθcosθcos2θ=1-2sin2θlet us consider right…

Q: Determine the following statement is true or false.  For any,  theta,cos^2(theta)1-tan^2(theta))=1

A: Given statement is cos2θ-tan2θ=1 To check whether the given statement us true or false. So, we have,…

Q: 4. Prove the following identity: 1 - tan?a cos2a %3D sec?a Sin(420) b sin7d

A:

Q: Find the exact value of each of the remaining trigonometric functions of 0. tan 8 = 3 '4' cos 0 <0

A: Given problem:- Find the exact value of each of the remaining trigonometric functions of θ tan(θ) =…

Q: Evaluate the following trigonometric functions exactly if they are defined. Otherwise, write…

A:

Q: Evaluate the following: 1. sin (20), if sin (0) =and <0 <

A: We have to find the given trigonometric function.

Q: Which of the following is equivalent to sinθcosθsecθcotθ for all values of θ for which…

A: sin θ cos θ sec θ cot θ=sin θ cos θ×1cos θ×cos θsin θ=cos θ

Q: Verify the following trigonometric identity:cos4t−cos2t= sin4t−sin2t

A: The trigonometric identities can be verified by solving the left hand side and right hand side…

Q: Use the given conditions to find the values of all six trigonometric functions. (If an an sec(x) =…

A:

Q: II. Verify the following trigonometric identit 7. sin 0 csc 0 cot 0 = 1 tan 0

A:

Q: Determine the guadrant in which the terminal side of 0 lies (a) cos 0 0 (Choose one) (b) sin 0 < 0…

A: Given that  A) cosθ&lt;0 and sinθ&gt;0 b) sinθ&lt;0 and tanθ&lt;0

Q: Prove the following identity: 1- tan? e cos 20 = sec e

A: solution:-cos2θ=1-tan2θsec2θ RHS=1-tan2θsec2θ        =1-sinθcosθ21cosθ2,      ∴tanθ=sinθcosθ &amp;…

Q: Use the given information sec α = -3, π/2 &lt; α &lt; π to find the exact value of the following: a.…

A: Given:             sec α = -3,            π/2 &lt; α &lt; π        cos α = =1sec…

Q: Prove the following identities: sine tan e = sec e cosec 0 + cote 1-cos e 1+cos e

A:

Q: following

A:

Q: Use the result (cos θ + i sin θ) 2 = cos 2θ + i sin 2θ to find trigonometric identities for cos 2θ…

A: The given result is: cos θ+i sin θ2=cos(2θ)+i sin(2θ)