### Verifying identities

Verify the identity in the attached document

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Verify the identity in the attached document

In any triangle ABC, prove that (b +c )cos A+(c +a) cos B+ (a + b)cos C=a+b+c

Verify this identity: Sec6x(SecxTanx) - Sec4x(SecxTanx) = Sec5xTan3x [include all the steps leading up to the verification]

Please see the attached file for the fully formatted problems.

1. Obtain the solution to the initial-value problem (1) for the given f(x, y), a, and b, and give the relations that define the nodal lines of w, if any. Let c=1 in each case. (e) f(x, y) = 1.05 sin 3x sin y - sin x sin 3y, a = pi, b = 2pi

1. Suppose that a boat leaves Jacksonville traveling at a bearing of 110o. It goes 30.0 km, and then travels 100.0 km at a bearing of 170o. How far is it from Jacksonville? 2. Suppose that I am trying to judge the distance across a lake. I stand facing some house on the opposite shore. I turn 95o to the left, and walk 20 me

Please show each step of your solution. When you use theorems, definitions, etc., please include in your answer. 6. In each case solve (1) with boundary conditions (1b) changed as indicated, and for the specified f(x). Use a half- or quarter-range cosine or sine expansion, as appropriate... Please see attached.

2. A researcher randomly selects a sample of college students majoring in physics, chemistry, psychology, P.E., or English lit. He notes each student's major subject, and also whether that student is a blonde, a brunette, or a redhead. The data are as follows: Physics Chem Psych P.E. English Total Blonde 8 10 20 4 10 52

Solve each equation for exact solutions in the interval [0, 360]. Use either an algebraic method or a graphical method. 2 sin x -1 = csc x

The angle of elevation of a cloud from a point X m above a lake is A and the angle of depression of its reflection in the lake is 45 degrees. Find the height of cloud?

Find the fundamental period. 6 cos x - 4 sin 3x

Important Formulas and their Explanations (VI): Identities of Plane Trigonometry Pythagorean Relation Pythagorean Identities

Prove sec 2A + tan 2A = (cos A + sin A)/ (cos A - sin A) Express this as a sum of 2 trigo functions 2(siny)(sin5y) Prove (sin2A)^2 - (sinA)^2 = (sinA)(sin3A)

A man walks along a straight path at a speed of 4 ft/s. A searchlight is located on the ground 20 ft from the path and is kept focused on the man. At what rate is the searchlight rotating when the man is 15 ft from the point on the path closest to the searchlight?

Please see the attached file for the fully formatted problems.

There are 3 problems. The first and second problem are with the dotted lines both are division problems. I am looking for the expression for each. 1) Sin(x + B) + cos( x - B) --------------------------- = Cos(x + B) - sin(x - B) 2.) Tan2x + sin2x = -----------------

1) 2 tan (theta /2)= 2) 2 tan theta Sin ^2 (theta /2)= 3) 2 Cos (45 + x) Cos (45-x)= 4) (Sin 3 x - 3 Sin x )/ ( Cos 3 x + 3 Cos x) = 5) 2 tan (theta /2) / { 1 + tan ^2 (theta /2) } = 6) Find the least positive value of theta such that tan (45+ theta ) - 3 tan theta =2

I have a attachment of 2 problems of which I am trying to solve. For both of these problem, I am to derive an expression. Derive a Trigonometric expression. Please see attached.

Solve for x: sin x = cos x Solve for x: cos x - 6 sec x = 1 Both are 0 is less than or equal to x and x is less than or equal to 2 Pi

Given sin x=-1/8 and tan x < 0, find sin 2x (without using a calculator).

Given sin x=-1/8 and tan x <0, find sin 2x.

Prove: (1+ cot^2 θ/1+tan^2 θ)=cot^2 θ

Latitude presents special mathematical considerations for cartographers. Latitude is the north-south location on the earth between the equator and the poles. Since the earth flattens slightly at the poles, a nautical mile varies with latitude. A nautical mile is given by N(e) = 6066 - 31 * cosine 2e. e represents the latitude in

A V-gauge is used to find the diameters of pipes. Look at the figure in the attachment, the measure of angle AVB is 54°. A pipe is placed in the V-shaped slot and the distance VP is used to predict the diameter. a. Suppose that the diameter of a pipe is 2 cm. What is the distance VP? b. Suppose that the distance VP is 3.9

1. Two cars with new tires are driven at an average speed of 60 mph for a test drive of 2000 miles. The diameter of the wheels of one car is 15 inches. The diameter of the wheels of the other car is 16 inches. If the tires are equally durable and differ only by diameter, which car will probably need new tires first? Why? 2

I need help with the following problem. For the range 0.1 < or = x <or = 0.2, plot the following function. cos (3x)/sin (2x) I really don't know where to begin. thanks

The figure below shows the graph of a sine function - y is a function of θ, with θ measured in degrees. For this function state: a. its Period b. its Amplitude c. its Phase Shift from the sine function y = sin2x d. the Equation of the Function Answer in degrees also please Please see the attached file for t

A) y'''' - 11y''' +45y"-81y'+54y = (t+1)e^(3t) b) y''+y=tcost

Evaluate (be careful if n=m) ∫ 0 --> L sin(n pi x/L) sin(m pi x/L) dx for n>0 and m>0. Use the trigonometric identity 2 sin a sin b = cos(a-b) - cos(a+b) Please see the attached file for the fully formatted problems.

1. A flat is machined on a circular bar if 15 mm diameter with a central depth of 2 mm. Find the area of cross-section of the finished bar. Q2. The diagram shows 5 holes equally spaced round a pitch circle of diameter 100 mm. Calculate the co-ordinate dimensions (i.e. the x and y co-ordinates) of the hole centres relative to