9. Partner each expression with an equivalent expression to make an identity equation. Then classify the equations into two groups. Explain the similarities and differences as to why you grouped them the way that you did. cos(x), sec(x), , sec-(x), (secx)-, sec-(x-), arccos(x), arcsec(x)

Q: How would I simplify cos3x+sin2x * cosx

A: Remember:

Q: Express cos(tan-(2x + 3)) in an algebraic form.

A:

Q: * Evaluate. [12 [20x cos(5x² - 1)]dx

A: The given integral is   ∫20xcos5x2-1 dx We solve the integral using proper substitution .

Q: Write sin*x + cosx in terms of first powers of cosine.

A: Given, sin4x+cos2x

Q: Find the value →21. csc (sec- 2) + cos (tan¬1 (– V3))

A:

Q: Find an algebraic expression for cos(arcsin(2x)).

A: To Find an algebraic expression for cos(arcsin(2x)).

Q: If cos (-x) =, find sin(-x).

A:

Q: Find all solutions to the equation. 4 sinx=5-4 cosx

A:

Q: Graph off (x) = cos2 x - 2 sin x/4.

A:

Q: Evaluate cos tan Vx² + 1

A: We have to evaluate the given trigonometric function.

Q: Find all exact solutions to the equation arcsin(2x)+arccos(x) 6 X=

A:

Q: Find the first derivative: y = 3 arcsin(cos 2x) O -7 О-5 O-4 O-3

A:

Q: (cos 5x -sin 5x) dx cos²5x S

A:

Q: If sinx^2 =a/b find cos(90-x)

A: See the details solution in below I am consider  sin(x^2 )

Q: State the half-angle identities used to integrate sin x and cos x.

A: Half Angle Identities are the formulae/relationships used in trigonometric functions to reduce the…

Q: Determine whether the equation is an identity. If it is, explain how. (sinx + cosx)^2 = 1

A: An identity can be defined as an equality relation A=B, such that A & B contains some variables…

Q: Write cos*x in terms of first powers of cosine. 4

A: cos4x

Q: Use even-odd identities to find the value. If sec(-a) =-1.21, find csc a -

A:

Q: arctan[2 cos(³)] is equal to: COS

A: Given that the expression arctan2cos32. Find the value of arctan2cos32.

Q: Solve the equation: tan x + sec2 x = 3, 0 ≤ x < 2π

A: Consider the following trigonometric equation: tanx+sec2x=3 Substitute sec2x=1+tan2x in the above…

Q: if sin= -2/3 find csc ?.

A: We have to find value

Q: If y = sin2x sin3x sin4x then find y"

A: Explanation of the answer is as follows

Q: Prove the identity. cosx sin (x+ y) – sinx cos (x+y)= sin y

A:

Q: Find sec 0 if cos 0 ||

A: Our Aim is to find sec θ given that cos  θ=13

Q: Find cos θ⁡ whose terminal side passes through the point (-3,4).

A:

Q: The simplified form of [csc(-x) + cos(-x)] · [9 sin² æ sec? æ]

A: The simplified form of [csc(-x) + cos(-x)] [9 sin²x sec² x]

Q: Write cos 3x cos 2x - sin 3x sin 2x as a single cosine.

A: Given expression is cos3xcos2x-sin3xsin2x. To write the given expression as a single cosine. We know…

Q: Verify. esc (x) [I-cos(2x)] = 2 sin (x) SC

A:

Q: How to graph sin(x) + sin(2x)?

A: Given: The objective is to plot graph for the function sin(x)+sin(2x).

Q: Evaluate: " sin7 cos4 dx

A:

Q: 3. sec-1 -tan

A: Given,

Q: Graph One period y = 5 cos (3x – 27) y = tan(}a)

A: If equation of function is Y = a cos(bx-c) , where a is the amplitude of the function, the period of…

Q: *cosx= 24 sinxyo, cos (x+5") 25

A: Given: cosα=2425, sinα>0 To determine: cosα+5π6

Q: cos² (x) sin (x) dx

A:

Q: Evaluate: " sin' (-) Cos3 dx

A:

Q: cos2 θ - cos2 θ is equivalent to?

A:

Q: Partner each expression with an equivalent expression to make an identity equation. Then classify…

A: given expressions are                            sinx, cscx, 1sinx, cscx, cscx-1, cscx-1, arcsinx,…

Q: Find all solutions of the equation 1 COSX=

A:

Q: If tan(x)=12/11(in Quadrant-I), find cos(2x)=

A:

Q: Evaluate  sin2x*cos2x dx

A: Given that: ∫sin2x.cos2x.dx

Q: Use even-odd identities to find the value. If sec(-a) = -1.21, find csc a-

A:

Q: If roots of equation 3x² + 5x + 1 = 0 are (sec6 (cosec0₂ - cot0₂), then find the equation wh (sec₁ +…

A:

Q: Simplify: 1−cos2 x/cos x−sec x

A: To simplify the following expression (1−cos2 x) /(cos x−sec x)

Q: Use basic identities to simplify cos3x + sin2x cos x

A: We need to simplify the following expression cos3x+sin2xcosx Formula Used : sin2x = 1-cos2x

Q: Evaluate: ( cos$ 2xdx sin 2x

A:

Q: Use the addition formulas to derive: cos (x -) = sinx

A: The given equation is cosx-π2=sinx

Q: Find sin (x- π/2) if cos x=0.65

A: On solving this we will get

Q: Express cos(tan-1(2x + 3)) in an algebraic form.

A: Given costan−12x+3 We have to write costan−12x+3 in an algebraic form. Let θ=tan−12x+3…

Q: simplify in terms of sine and cosine 2+tan2x - 1=f(x)2 sec2x

A:

Q: cos8x -dx sin4x

A: We use some trignometric identites.  Sin2 x + cos2 x =1 Sin(2x) = 2cos(x)sin(x)

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.