Question

Cos(п-a) - cos(-a),a=п/4

Answer 1

$cos( \pi-\frac{\pi}{4})-cos(-\frac{\pi}{4} )=-cos( \frac{ \pi }{4} )-cos( \frac{ \pi }{4} )=-2cos( \frac{ \pi }{4} )$
$-2* \frac{ \sqrt{2} }{2} =- \sqrt{2}$

Answer 2

To evaluate the expression for the given value of "a," we first need to express "п" in terms of "π" since "п" is not a recognized mathematical constant.

Let's assume "п" is meant to be the Greek letter "π" (pi), which represents the mathematical constant approximately equal to 3.14159.

Now, we can proceed with the calculation:

1. Convert "п" to "π": п = π.

2. Substitute the value of "a" in the expression: a = π/4.

The expression becomes:

cos(π - π/4) - cos(-π/4)

Now, we'll evaluate the individual terms:

cos(π - π/4): We know that cos(π - θ) = -cos(θ). So, cos(π - π/4) = -cos(π/4).

cos(-π/4): The cosine function is an even function, meaning that cos(-θ) = cos(θ). So, cos(-π/4) = cos(π/4).

Now, the expression becomes:

• cos(π/4) - cos(π/4)

Now, simply perform the arithmetic:

• cos(π/4) is the same as -√2/2.

Therefore, the final result is:

-(-√2/2) - √2/2 = √2/2 + √2/2 = √2

So, Cos(п-a) - cos(-a) = √2 when a = π/4.