Write each expression as an equivalent algebraic expression involving only x. (Assume xis positive.)   sin (2 cos-1 x)

Q: FIND THE EXACT VALUES OF EACH EXPRESSION sin2 150º + cos2 150 º

A: sin2 150º + cos2 150 º

Q: Which expression is equal to cos(6t)?

A: Recall:  cos(2t)=cos2(t)-sin2(t)     Given,   cos(6t)

Q: Write the given expression in terms of x and y only. tan(sin-(x) + cos-(v))

A:

Q: Find the exact value of each expression .cos-1(-1).

A: To find the exact value of cos-1-1. Solution: Principal range of the cos-1x is 0,π. Evaluating the…

Q: rewrite sin(x+pi/4) in terms of sin(x) and cos(x)

A: sin(A + B) = sinA cosB + cosA sinB

Q: sin(A) tan(A)+ cos(A) = COS

A: Given- sinAtanA+cosA To Simplify- The above trigonometric expression. Identity Used- sin2A+cos2A=1.…

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

A:

Q: cos2e sin20 + csc 0 sin e

A:

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: Write the given expression as an algebraic expression in x. sin(2 tan-'(x))

A: Trigonometric

Q: Write the given expression as an algebraic expression in x. cos(2 cos-1(x))

A:

Q: Rewrite 4sin(×)as A sin (×+θ) A= Θ=

A: Given,           4sin(x)

Q: Simplify the identity, show all steps. sin(x) 1+cos(x) 1. 1+ cos(x) sin(x)

A: We use identities  sin2(x) +cos2(x) = 1  1/sin(x) = csc(x)

Q: Verify that each equation is an identity.  (1-cos x / 1+cos x) = (cot x - csc x)^2

A: Multiply by (1-cosx) in numerator and denominator. Note: 1-cos^x=sin^2 x [Pythagorean identity]

Q: Write each expression in terms of sines and/or cosines and then simplify.…

A: 1) Given expression,                   sinXcscX - secX cosX

Q: Solve each equation for x if 0 # x , 2p. Give your answers in radians using exact valuesonly.   4…

A: The given equation is 4cos2x-4sinx-5=0. Solve the above equation as follows.

Q: each expression. sec x с. 1+cos2 x

A:

Q: Factor each expression completely. (a) x² - y2 (b) cos? e - sin² e

A: We know that identity a2-b2=a-b(a+b)

Q: If cos(a) = 2/3 , sin(b) = -3/5, P(a) in Q1, P(b) in Q3,  find cos2(b)

A:

Q: Write an equivalent algebraic expression that involves x only.      tan (cos- 1 x)

A: Evaluate tancos-1x       ...(1)

Q: simplify the given expression  sin(2x)cos(6x)-sin(6x)cos(2x)

A: Explanation is given below...

Q: #6. Write each using only the indicated function a) cos? x - 2 sin x; use sine

A: We need the Pythagorean theorem

Q: Write the expression as an equivalent algebraic expression involving only x. (Assume x is positive.)…

A:

Q: Write an expression that gives all solutions to the equation. cos x – sin x = = V2

A: cosx-sinx=2

Q: Write each expression as a single trigonometric function.   cos 5x cos x - sin 5x sin x

A: cos Acos B-sin A sin B=cos(A+B)

Q: Rewrite the expression algebraic expression in x: -1 tan cos as an

A: We know that ,  In a right triangle ,  cos A = adjacent / hypotenuse  And  tan A = opposite /…

Q: Write the expression cos(arccot x) in algebraic form.

A: The given expression is cosarccot x.

Q: Which of the following values of x is a solution to the equation sinx+cos x=1

A: Given:        Equation sinx+cosx=1    squaring on both sides we get         sinx+cosx2=12…

Q: Find the exact value of each expression, if it is defined. (If an answer is undefined, enter…

A:

Q: Evaluate the expression cos-1(sin(pi/3))

A:

Q: Perform each indicated operation and simplify the result so that there are no quotients. (1/1 + cos…

A: Subtract using LCD

Q: Write an expression that gives all solutions to the equation. sin x + cos x = - 12 + ka + 2k7 + ka…

A: Explained below

Q: Simplify the expression. cos(2 tan(x))

A: Use the cos double angle formula and then proceed, solve the problem as shown below.

Q: Evaluate each expression, express your answers in radian. 1. cos-1 2. sin-(-1)

A: topic - Inverse trigonometric functions

Q: Write the expression in the standard form a+bi. 4 cos + i sin 10 10

A: Given : 4cosπ10 + i sinπ105

Q: 4Cos 4 cos 2x- 2 0 X= TT 8.

A:

Q: evaluate the expression cos-1(sin(pi/6))

A: evaluate the expression cos-1(sin(pi/6))

Q: Verify that each equation is an identity. Sin 2A cos 2A = sin 2A - 4sin^3 A cos A

A:

Q: Write the given expression as an algebraic expression in x cos(2 tan−1(x))

A: Given:

Q: Evaluate or simplify the given expression. cos(2 sinx)

A:

Q: Find the exact value of each expression, if it is defined. (If an answer is undefined, enter…

A:

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

A: Inverse trigonometric function:     cos(sec-1x2)We know cos(cos-11x2)

Q: Write − sin ⁡ ( 2 x − π 6 ) in the following form: cos ⁡ ( B x − C ) + D

A: graph of -sinx   graph of cosx+π2   It means that cosx+π2 and -sinx both have same graph.   In…

Q: Write cos(cot^−1 x) as an algebraic expression in terms of x.

A:

Q: Rewrite cos (a + ) in terms of sin(x) and cos(x).

A:

Q: verify that each x value is a solution of the equation. 2sin^2(x)-sin(x)-1=0 a) x=5pi/2 b) x=…

A:

Trigonometric Identities

Trigonometry in mathematics deals with the right-angled triangle’s angles and sides. By trigonometric identities, we mean the identities we use whenever we need to express the various trigonometric functions in terms of an equation.

Inverse Trigonometric Functions

Inverse trigonometric functions are the inverse of normal trigonometric functions. Alternatively denoted as cyclometric or arcus functions, these inverse trigonometric functions exist to counter the basic trigonometric functions, such as sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec). When trigonometric ratios are calculated, the angular values can be calculated with the help of the inverse trigonometric functions.