sin(x + y) = sin(x) cos(y) + cos(x) sin(y)cos(x + y) = cos(x) cos(y) − sin(x) sin(y)23a. Find an exact value for sin(75◦).Note: some calculators will do this for you. You must do this using the identities above, and you must show your work.23b. Simplify the following expression: cos(270◦ − θ)

Q: (e" -e¹"), then write: e¹ and e¹*. 1 If cos(x)= os(x) = -(e* + e^ª) and sin(x) = -— (e“ - e²"), e™“)…

A: We have to find the values of

Q: cos(7) -dp. 1 – cos²(x) 1. Evaluate

A:

Q: Using the substitution u = sin (x), or otherwise, find the exact value of %3D J sin° (x) cos (x) dx.…

A:

Q: 2. (a) (b) Simplify the following expressions. tan(-0) sin(7-8) 1+cos (2+0) cos(+0)

A: The given expressions,(a) (b) .The aim is to simplify the given expressions.

Q: (14) Prove the following identity cos(x + y) + cos(x - y) = 2 cos(x) cos(y). Make sure you show all…

A: We have to prove the given identity- cos(x + y )+cos(x - y) =2cos(x) cos(y).

Q: sin(2x) = 2 sin(x)is not an identity. Do not use a calculator. Q4: Compare the values of sin(x +y)…

A: The trigonometric equation to be proved is given as,

Q: Simplify cos(x + y) + cos(x – y) 1. cos x cOS Y 2. 2 cos x 3. 2 cos x sin y 4. 2 cos y 5. 2 cos x…

A: We have to simplify the following. For this we can use the trigonometric indentity formula . I have…

Q: Is the function f(x)=sin(3x)+cos(tan x) even, odd, or neither? Why?

A: Recall: A function f(x) is even if  f(x) =f(-x). A function f(x) is odd if f(x)=-f(-x)

Q: State the sum and difference formulas for the cosine. cos (x + y) = cos (x) cos (y) - sin (y) sin(x)…

A:

Q: 1. Consider the function g(x, y) = cos(xy) + sin(x - 2y)

A: INTRODUCTION: The formula of directional derivative of a function f(x,y) at a point (a,b) is given…

Q: Suppose that a and ß are in the first quadrant, sin(a) = , and sin(B) = . What is sin(a + B)?

A: cos2α=1-sin2α sinα+β=sinαcosβ+cosαsinβ