Decide whether each statement is possible or impossible. (a) sin u = 1.5 (b) sec u = 4 (c) tan u = 10,000

Q: cos^2 t (1+ tan^2 t) Use trignometric identieties to write each expression in terms of a single…

A:

Q: Use sum or difference itentity to find the exact value, tan 75° A.) V3+2 B.)-3-2 C.) J3-2 D.)-3+2

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Q: Find the exact value of the expression. tan(sin−1(12/13))

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Q: The value of the expression cos" a – tan² æ - 8 + sin² x + sec² x is, O 16 tan a O -6 O 16 O 16 sec…

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Q: Simplify the trigonometric expression. cos3(x) sin2(x) cos(x)

A: Given:

Q: Use the formulas for lowering powers to rewrite the expression in terms of the first power of…

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Q: find the exact value of each expression.

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Q: Use a right triangle to simplify the given expression. Assume x 7 0. cos 1tan-1x 2

A: Now let Now it can be represented by using right angled triangle as,

Q: Tan (Cos (-)) Evaluate and give exact answer; 6

A: Given:Tancos-1-32

Q: What is the exact value of sin(-150°)? -|N 1 7개 6 아틀

A: Find out the exact value of the given trigonometric function.

Q: Simplify the trigonometric expression. tan x cos x csc x X

A: Given: y=tanxcosxcosecx we know that tanx=sinxcosxcosecx=1sinx

Q: Find the exact value of the expression, if possible. (If not possible, enter IMPOSSIBLE.) sec[arcos(…

A: Given that: secarccos-34

Q: 11. Find the exact value of each expression. a) sin-1 () 2 b)sin(tan-(-V3)

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Q: s-() Find the EXACT value of tan( cos¯ + sin- (1),u

A: Given query is to find the value of the expression.

Q: Simplify the expression tan2⁡x(csc2⁡x−1). 1 tan2⁡x cot2⁡x -1

A: We have to find the simplification

Q: Rewrite the expression [sin(α + β) - sin(α - β)]/[cos(α + β) + cos(α - β)] as a simplified…

A: Given expression, sinα+β-sinα-βcosα+β+cosα-β

Q: The equation sin(sin-1(x))=x holds for any real number x a. true b.false

A: domain of sin-1(x)  is  [-1, 1]

Q: Let sin t = a, cos t = b, and tan t = c. Write the expression sin(-t - 2π) + cos(-t - 4π) - tan(-t -…

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Q: Solve each equation on the interval 0 ≤ θ<2 π. tan (2θ ) + 2 cosθ = 0

A: Given: The equation tan2θ+2cosθ=0 on the interval 0≤θ≤2π, To determine: The solution of given…

Q: The expression 2 tan(x) sin(x) + 5 sec(x) simplifies to A sec(x) - B cos(x), determine A and B.

A:

Q: Use a double-angle formula to rewrite the expression. 16 sin x cos X

A:

Q: Solve each equation on the interval 0 ≤θ < 2π . secθ = tan θ +cot θ

A: Given: secθ = tan θ +cot θ

Q: The value of the expression cos? x – tan? x – 8 + sin² x + sec² x is 2 -

A: Given expression : cos2x -tan2x-8+sin2x+sec2x We need to evaluate determine the value of above…

Q: Complete the proof of the identity by choosing the Rule that justifies each step. tanʼx (csc?xr- 1)…

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Q: 12 Find the exact value of tan(sin- (-) | 13

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Q: Find the exact value of the expression. tan(an- (금)) tan( sin-1 25

A: Given  To find the exact value of the expression  tansin-1725 Let  θ=sin-1725sinθ=725 Using…

Q: Find the exact value of each expression: (i) sin (1) (ii) tan-1 V3

A: (i) Given-  sin-11  (ii) tan-13 To find- The exact value of the expression.

Q: Use the fundamental identities to fully simplify the expression. sin(x) cos(x) sec(x)

A: Given:

Q: 49. Write tan x in terms of sec x.

A:

Q: Write the first expression in terms of the second if the terminal point determined by t is in the…

A: Given expression is

Q: Which of the following is a value of tan 0 if V3cos 0 – sin 0 = v2? -V3 + 2 V2 + 3 Option 1 Option 2…

A: Use trigonometry

Q: Use a double-angle formula to rewrite the expression. 18 sin x cos x

A: We have to find function

Q: Simplify the expression. tan(sin 'x) a. . sin(tan-'x) a.

A: use pythagorean theorem and right angle triangle.

Q: Decide whether the statement is possible or impossible. sin(theta)=0.5 and csc(theta)=-0.5

A: Recall: sine and cosine function are positive in second quadrant. sin(θ) =1cosecθ

Q: Use the figure to find the exact values of sin(2u), cos(2u), and tan(2u). (4, -7) sin(2u) -0.87 |x…

A: Topic:- trigonometry ratios

Q: Evaluate csc(cos^-1(tan(sin^-1(a/b)))) when a/b is a positive real number

A: we have to evaluate csc(cos^-1(tan(sin^-1(a/b)))) when a/b is a positive real number

Q: 5. What is the exact value of tan 105°? O -24 V3 O-2-V3 O 2- V3 O 2+ V3

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Q: Evaluate csc(cos^-1(sin(tan^-1(a/b)))where ab is a positive real number.

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Q: Prove the identity. sin (x+y)+ sin (x-y) =2 sinx cosy Note that each Statement must be based on a…

A: Consider the identity  sinx+y+sinx−y=2sinxcosy

Q: Let sin t = a, cos t = b, and tan t = c.Write the expression sin(-t - 2π) + cos(-t - 4π) - tan(-t -…

A: Since we have been given that sin(t) =a , cos(t)= b and tan (t) =c.Our Aim is to write the…

Q: Determine whether the statement is true or false. tan−1(x) = sin-1(x)/cos-1(x)

A: Given,

Q: Find the exact value of each expression.   a)  tan(Sec-14)   b) Sin(2 Sin-1(3/5))

A:

Q: Use a sketch to find the exact value of the expression sin (tan-1 7/24)

A: sintan-1724 Now let, tan-1724=θ⇒tanθ=724 Now consider the right angled triangle, Now by using…

Q: Simplify the trigonometric expression. 3 sin(x) sec(x) tan(x)

A: Given expression is

Q: -1 Evaluate sin ( tan giving your answer as an exact value (no decimals)

A:

Q: Simplify the following expressions. sin (tan-¹ ( =)) = sin (2 tan-¹()) =

A: sintan-1x2

Q: Rewrite tan( sin¬'u) as an algebraic expression in u. n(sin¨'u) = [] - 1

A:

Q: Rewrite the expression in terms of the given function or functions (sec x + csc x)(sin x + cos x) -…

A: tanx=sinxcosxsecx=1cosxcosecx=1sinxcotx=1tanx2sinxcosx=sin2xsin2x=2tanx1+tan2x

Q: Use a calculator to solve the equation tan2 x - 3 tan x + 1 = 0 correct to four decimal places, on…

A: To solve the equation,  tan2x-3tanx+1=0 By using substitution, Let u=tanx, u2-3u+1=0

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.