Q:Prove the following trigonometric identities: 0(1-sir'e) Sec'e =1 (i)cos'e(1+ tan'e) = 1.

Q: 6. Find the exact of the following, if the exist. a. sec- 2 C. cot e. cos (arccsc12) b. csc-1 1 d.…

A: 6) a) Given:   sec-12            let sec-12=x then x=π4 b) csc-11    then x=π2

Q: Given: cos A= -, sin x = - 3, e is in the third quadrant, and x is in the fourth quadrant; evaluate…

A: Given, cosθ=-45  where 180°<θ<270°We know that ,sin2θ+cos2θ=1sin2θ+-452=1sin2θ+1625=1Subtract…

Q: Set up a trigonometric ratio from ZH to solve for x. H U 14

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Q: Express (cos(a@) ti sin 4i sin (a@) in exponential form

A:

Q: Differentiate the following inverse trigonometric functions : 1) y =-2 sin-1x 2) s (t) = - cos-1 t

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Q: 5. Find the values of a and b such that dx tan 1 + sinx a + b . %3D

A: We need to integrate ∫11+sinxdx

Q: 11. Evaluate the exact value of each of the following trig e> a) tan-(-V3) b) sec (sin" (-))

A: Answer and explanation is given below

Q: 6. Explain the steps in verifying that the following equation is an identity. sec x sin x = cot x…

A: We have given equation  Taking left side of equation  LHS = secxsinx-sinxcosx           =…

Q: Find sin(2x), cos(2x), and tan(2x) from the given information sec(x) = 4, x in Quadrant IV %3D…

A: Given: secx=4, x in Quadrant IV   We know that; The trigonometric identities; 1). sin2x+cos2x=1 2).…

Q: V2 -, sin 0 > 0, find the exact value of each of the remaining five trigonometric 2 Given that: cos…

A: Trigonometric Functions: Trigonometric functions are simply defined as the functions of an angle of…

Q: find sin ). co ), aud tan for each gueton Sin X = 4 and x is ふ quadrant

A: We have to find  Sin(x/2) ,Cos(π/2), and tan(π/2); For sin(x) = 1/8 and x is in first quadrant.

Q: 2. Write sin(t) in terms of cos(t) for t when t lives in quadrant III

A:

Q: Find sin(2x), cos(2x), and tan(2x) from the given information. sec(x) = 6, x in Quadrant IV %3D…

A: Given, sec(x) = 6,    x in 4th quadrant

Q: Va? – x²

A:

Q: From the formula for cos (t + t) find cos (2t) in terms of sin t.

A:

Q: 15 What is the exact value of tan (sinr) where r 17 Provide your answer below:

A: Solving the problem by finding the value of the function.

Q: (x^2)cos^2 x - (x^2)sin^2 x = ? Is this a double-angle trigonometric identity?

A: we have evaluate the following . We can use double angle trigonometric identity

Q: ) Use Euler's formulas to calculate | cos(ax) sin(bæ)dx for a > 0 and b > 0.

A:

Q: what is y' of y=sin-1(cos x)

A:

Q: e or sin 1 2 and tan 2 cos .2

A:

Q: d) Verify the identity sin 0 tan 2, 1+ cos e

A: To prove:

Q: What is the exact value of cos (tan¬'m) where m = :? 12 Provide your answer below:

A: if m=512 To find: the value of costan-1mSolution :let…

Q: one of sin x, cos x, and tan x is given. Find the othertwo if x lies in the specified interval.

A: You know:

Q: Using appropriate substitution, ſ sin1º(x)cos³(x)dx is equal to: an

A: By using integration by substitution.

Q: 1) Use Excel to plot both of sin(x), cos(x) at the same plot, where: 0<x <2n.

A: To find- Use Excel to plot both of sinx, cosx at the same plot, where: 0 ≤ x ≤ 2π.

Q: V3 and 0 in QII sin 0 %3D

A:

Q: 1 + sin² (x) dx sint(x)cos (x)

A: We have to find the integral.

Q: Use a ratio identity to find tan θ given the following values: sin θ = 3√10 over 10 and cos θ = √10…

A: Given:…

Q: 1. cos x |? ecosx sin xdx

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

Q: Approximate to four decimal places, when appropriate.

A: To evaluate,

Q: 3) Given that tan(0) = - and cos(0) > 0, find the exact values of sin(0), cot(t), and csc(0).

A: Given :   To find :

Q: 5) coS I sin rdr

A:

Q: 13. Prove the following trigonometric identity until LS = RS %3D sec20-tan?0 %3D Csc e sin20 csc 0

A: We can prove the identity as below.

Q: Complete the steps by applying trig identities to show that the left hand side of the equation is…

A: To prove : tan2x - sec2xcos x = -sec x

Q: 4. Use appropriate trigonometric identities to determine 1 dx 1- cos? x (i) (ii) Scos 7x dx (ii) S(1…

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Q: 4. y = Arc tan² x³ 5. Ø = Are cot 2x

A:

Q: Suppose that sin u > and cos v = 13 such that bot and v in the and quadrant. as are • What is the…

A: Here, the given values are: sin u=513 &amp; cos v=-35 So, u and v are both in 2nd quadrant.

Q: What is the value of d. (sin x3 dx cos x²)? COS

A:

Q: express the given quantity in terms of sin x andcos x. cos (π + x)

A: Given expression is cosπ+x. To express the given expression in terms of sinx and cosx. Solution: We…

Q: 15. Explain the steps in verifying that the following equation is an identity. sec a sin e sin a cot…

A:

Q: Find, correct to six decimal places, the root of the equation cos x = x

A: To find :                          The root of the equation cos x = x up to six…

Q: Verify the identity. sin(0) 1 - cos(e) csc(e)cot(e)

A: Given,

Q: Evaluate the six trigonometric functions at t = 4π/3. Only exact values,

A: The given angle is t = 4π3   which is 240° the angle is in the third quadrant. in third quadrant the…

Q: Differentiate the following inverse trigonometric functions : 1) y -2 sin-1x 2) s (t) =-cos-1 t

A: We will ise tha fact that  Derivative of sin-1(x) is 1/√(1-x2) and that of cos-1(x)=-1/√(1-x2). And…

Q: 1-Show that a +B sina – sinß = 2cos(- 2 a -B

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

Q: Write 4 coS x sin x in the form R cos(x – a) with -T < a < T. Round to three decimal places.

A: Consider the given function.

Q: Determine the value of sin a + cos a for a = 20 degrees. %3D

A: Here we have to evaluate the value at given x.

Q: Solve for the exact solutions of the given trigonometric equation in the interval 0 < x < 27. tan()…

A: