Is it ever possible that cos (a−b)=cos ⁡a−cos ⁡b? why or why not?

The given equation is never possible i.e cos ( A - B ) ≠ cos A - cos B

Step-by-step explanation:

Given as :

Is cos ( A - B ) = cos A - cos B

To check this possibility , Let us put the value of angle A and B on both side of equation

Now, Let A = 60°    and  B = 30°

From Left hand side equation

cos ( A - B ) = cos ( 60°  - 30° )

Or, cos ( A - B ) = cos 30°

∴   cos ( A - B ) =

or, cos ( A - B ) = 0.866

From Right hand side equation

cos A - cos B  =  cos  60° - cos  30°  

Or,  cos A - cos B  =   -  

∴,  cos A - cos B  = 0.5 - 0.866

I.e  cos A - cos B  = - 0.366

So, Left hand side ≠ Right hand side

Since while equating the values of angle A and b in the given equation on both sides, we get that the value of both sides are not equal , Thus we can say that the given equation is not equal to each other .

Hence given equation is never possible i.e cos ( A - B ) ≠ cos A - cos B Answer

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation:

27 + 13x + 15 = (x + 5)( =

step-by-step explanation:

27 + 13x + 15 = (x + 5)( = 27 + 13x + 15 = (x + 5)( = 27 + 13x + 15 = (x + 5)( =