Chapter 4.2, Problem 57E

To determine

To find: Whether the given expressions are equal or not.

Answer to Problem 57E

The given expression $\cos 1\cdot 5\ne 2\cos 0\cdot 75$ is not equal is verified.

Explanation of Solution

Given information:

The given expression is $\cos 2t\ne 2\cos t$ approximating $\cos 1\cdot 5$ and $2\cos 0\cdot 75$ .

Calculation:

Calculate the value of $\cos 1\cdot 5$ .

Using the calculator first set the mode os the calculator to radian mode.

The calculator keystroke sequence is as.

  $\boxed{\cos }\boxed{(}1\cdot 5\boxed{)}\boxed{\text{ENTER}}$

The displayed on the calculator is $0\cdot 0707$ .

  $\cos 1\cdot 5=0\cdot 0707$

Calculate the value of $2\cos 0\cdot 75$ .

Using the calculator first set the mode os the calculator to radian mode.

The calculator keystroke sequence is as.

  $\boxed{(}2\boxed{\cos }\boxed{(}0\cdot 75\boxed{)}\boxed{)}\boxed{\text{ENTER}}$

The displayed on the calculator is $1\cdot 4634$ .

  $2\cos 0\cdot 75=1\cdot 4634$

From the above values it is clear that $\cos 1\cdot 5\ne 2\cos 0\cdot 75$ .

Therefore, the given expression $\cos 1\cdot 5\ne 2\cos 0\cdot 75$ is not equal is verified.