Prove each identity  ( sec x-1 ) ( sec x+1) = tan 2 x

Q: 1. Find the average rate of change of k(x)= -x² over the interval [4,8]. Write your answer as an int...

A: Given :           k(x) = -x2  ,  4,8  

Q: For each equation, identify the period, horizontal shift, and phase. Do not sketch the graph.       ...

A: Given that: The equation is y = cos πx + π4.  

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

A: we have to show that the following statement is true . 1-cosθsecθ=sin2θ

Q: (4,127 fih thon z<12, 57 and angle

A:

Q: Prove that each of the following identities is true.   1+  cos x / 1- cos x  = (cosec x + cot x ) 2

A: we have to prove that the identity is true 1+cosx1-cosx=(cosecx+cotx)2

Q: (8/cos(x)+1)+(8/cos(x)-1)=−16 csc(x) cot(x) Steps that is takes to get from (8/cos(x)+1)+(8/cos(x)-1...

A: Given that LHS is 8cosx+1+8cosx-1.

Q: Lady calculus is waiting for her husband she can see him from the window, riding on his horse toward...

A: Consider the following figure: Consider Person L is at Point A and Person S at point C.

Q: Let cos A = with A in QII and find V13 sin(2A) = Preview TI Enter your answer as a number (like 5,-3...

A:

Q: Use half-angle formulas to find exact values for each of the following.     sin 75    0

A: Value of sin 75° using half angle formula.

Q: Prove the following identities.         cos theta tan theta = sin theta

A: We have to prove the identity: cosθtanθ=sinθ We know that tanθ=sinθcosθ

Q: Solve the equation for all solutions in the interval [0, 27t). 10) V2 Cos 2x = 1 %3D

A: Cosine function is positive in 1st and 4th quadrant.

Q: Prove:  1-cos^3A/1-cosA = cos^2A + cosA+1

A: 1-cos3A1-cos A=cos2A+cos A+1  

Q: Refer to right triangle ABC in which C = 90°. Solve each triangle.     a=4.37  0, c = 6.21

A: Given ∆ABC is a right angled triangle at C.  And a = 4.37 units c = 6.21 units To solve the triangle...

Q: Graph one completecycle of each of the following.   y = 2 sin 4 x

A: Consider the given function y=2sin4x

Q: if sin(x)= -9/41  and x is in quadrant III, find the exact values of the expressions without solving...

A:

Q: Find a cofunction with the same value as the given expression. sin(pi/6+x)

A: To find a cofunction of sinπ6+x

Q: Write the expression sin (cos-1 x) as an equivalent algebraicexpression in x only.

A:

Q: how do you figure out Coterminal angles

A: We have to tell you about, How do we figure out Coterminal angles.

Q: The height of an object (in feet) propelled upward is given by the equation, h(t) = - 16t +96t + 112...

A:

Q: Find angles theta between 0 degree and 180 degree ofor which the following are true tan theta = 1

A: we have to find the angle between 0 and 180 degree for which the following angles are true. tanθ=1

Q: For each equation, identify the amplitude, period, horizontal shift, and phase. Then labelthe axes a...

A: Given: y=3cos(12x+π3)

Q: Radius of a Circle If the sector formed by a central angle of 308 has an area of p/3square centimete...

A: Given: Central angle formed of a sector=308° Area of sector=π3 cm2 To find: Radius of the circle Sol...

Q: Name the reference angle for each of the following angles.   240 degree

A: Name the reference angle for each of the angle 240 degree.

Q: For each of the following problems, a point is rotating with uniform circular motion on acircle of r...

A: Given: r = 6 cm, v = 3 cm/sec

Q: Convert each equation to polar coordinates and then sketch the graph.      x2 +y2 =16

A: Consider the provided equation, x2+y2=16 Convert the above equation to polar coordinates. The polar ...

Q: Solve each equation for u if 0° &lt;= u , 360°.   4 cos u - 3 sec u = 0

A:

Q: Solve the triangle if it exists A= 132 degree a=22 b=16

A:

Q: Show that 2 cis 60 degree and 2 cis (-60 degree) are conjugates.

A: we know that cisθ=cosθ+isinθ

Q: In polar coordinates, each point is represented by a unique ordered pair.

A: In polar coordinate each point is represented by a unique ordered pair r,θ, where r=x2+y2 and θ=tan-...

Q: Question Solve the following equation exactly, where 0 < 0 < 2n. 3 tan (0) – 1 = 0 Select all correc...

A:

Q: Write each of the following in terms of sin theta and cos theta; then simplify if possible.   sec th...

A: Write each of the following in terms of sin theta and cos theta; then simplify if possible.

Q: Use the figure below to find the exact values of the half angles  find sin(theta/2), cos(theta/2), a...

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Q: Find exact values for each of the following, if possible.     sec 90  0

A: Given to find  sec90° The identity used here is  secθ=1cosθ

Q: Question Given that csc(0) = and 0 is in Quadrant II, what is tan(0)? Write your answer in exact for...

A:

Q: Reduce all fractions to their simplest forms. Convert all improper fractions to mixed numbers.: Find...

A: Given:

Q: Given that sin(a)= 3/4 and cos(b)= -1/3, with a and b both in the interval [pi/2,pi) find the exact ...

A:

Q: 3 cot2(y)(sec2(y) − 1) = 3 steps it takes to get from 3 cot2(y)(sec2(y) − 1) to 3

A:

Q: 15 Suppose that 0 is an angle in standard position whose terminal side intersects the unit circle at...

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Q: The notation f -1 (x) means the reciprocal of f(x).       True or false

A: Given f-1(x) is reciprocal of f(x).

Q: find the remaining trigonometric functions of theta based on thegiven information.  sin theta = 12/1...

A: Consider the following information: sinθ=1213 Use the following formula: sin2θ+cos2θ=112132+cos2θ=11...

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.