Find the exact value of each expression by applying trig formulas (Addition and Subtraction Formulas, Double-Angle, Half-Angle, and Product-Sum formulas): 1) cos² () - sin² () 2) cos 37.5° cos 7.5° Must show work and express your final answer as a fraction. Do not round your answer as a decimal.

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A: The given function is  f(x)=cos(x)-sqrt(3)x/2.

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A: Follow the procedure given below.

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A: Given :

Q: Find the​ consumers' surplus at a price level of p=​$150 for the​ price-demand equation below.…

A: Recall:  Consumer surplus=∫0x(D(x)-p)dx Given, p=​$150 p=​D(x)=300−0.05x

Q: Previous Problem Problem List Next Problem Solve the following equation in the interval [0, 2 π].…

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Q: Find the differential dy of the function y Provide your answer below: dy= dx = 5x4 + 4 4x + 3

A: y=5x4+44x+3Differentiate w.r.t xdydx=4x+320x3-5x4+444x+32

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Q: 3. Find 4 {0 21 jucosudu } using the properties of Laplace transform.

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A: To find for which intervals does the given values of f(x) are obtained.

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A: Here we have to find the area of shaded region.

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A: Let's find.

Q: lim- LIMIT VALUE: z²-16

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Q: 12 If [" f(x) dx = 19 and ' [₁ f(x) dx [R²F(x) f(x) dx = 4, find the following.

A: We can answer the question as below using the properties of definite integral.

Q: . find f'(x) if f(x) equals the given expression. a. log (x4 + 3x2 + 1) b. log (3x2 + 2)5

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Q: 7. Determine each of the following for the function, f(x, y) = 7x³y² - 2x + 3y. Show all ^~^ints.…

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Q: B) Estimate the next root of the function f(x)=x^3-x-1 using Muller method, let x0=1, x1=2, x2=1.5

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A: The given integral,       ∫cot4x csc4x dx

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