Prove that: cos(3π/4 + x) - cos(3π/4 - x) = -√2 sin x

Step-by-step explanation:

Consider

⇛cos{(3π/4) + x} - cos{(3π/4) - x}

We know that

cos x - cos y = 2sin{(x+y)/2}sin{(x-y)/2}

By, using this identity, we get

= -2sin[{(3π/4) + x + (3π/4) - x}/2] sin [{(3π/4) + x - (3π/4) + x}/2]

= -2sin[{(3π/4) + (3π/4)}/2] sin {(x + x)/2}

= -2sin[{2*(3π/4)}/2] sin (2x/2)

= -2sin(3π/4) sinx

= -2sin{x-(π/3)} sinx

= -2sin (π/4)sinx

= -2 * (1/√2) * sinx

= -√(2) * √(2) * (1/√2) * sinx

= -√(2) sinx

= RHS.

Hence, the value of cos{(3π/4) + x} - cos{(3π/4) - x} = -√(2) sinx .

Please let me know if you have any other questions.

b. would be the answer : )

step-by-step explanation:

step 1: add -16x to both sides.

16x−4y+−16x=64+−16x  

−4y=−16x+64

step 2: divide both sides by -4.

−4y /-4 = -16x + 64/-4

answer:   y=4x−16

hope i'm right

required rate of return = 0.166 = 16.6%

step-by-step explanation:

under the capital asset pricing model (capm), the required or expected rate of return for a particular security or asset is given using the formula:

required rate of return = risk-free rate + beta*(market risk premium)

we are given that;

risk-free rate = 4% = 0.04

beta = 1.4

market risk premium = 9% = 0.09

we simply plug these values into the above formula;

required rate of return = 0.04 + 1.4*(0.09)

required rate of return = 0.04 + 0.126

required rate of return = 0.166 = 16.6%