Chapter 13.8, Problem 74STP

To determine

Calculate the exact value of the expression.

Answer to Problem 74STP

The exact value is $\frac{\sqrt{2}}{2}$ .

Explanation of Solution

Given: It is given in the question that the expression is $\cos ({405}^{\circ })$ .

Concept Used:

In this, use the concept of trigonometric function and knowing the different signs of the four quadrant.

Calculation:

Here,

  $\begin{array}{l}\cos ({405}^{\circ })\\ \cos (360+{45}^{\circ })[\cos (360+\theta )=\cos \theta ]\\ \cos {45}^{\circ }\\ \frac{1}{\sqrt{2}}\\ \frac{1}{\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}}(Rationalise)\\ \frac{\sqrt{2}}{2}\end{array}$

Conclusion:

The value is $\frac{\sqrt{2}}{2}$ .