Question

Find an exact value of each expression, without using a calculator$\cos 62-\sin 28$

Short answer

The simplified value is$0$

Step-by-step solution

Step 1. Given information   

The given expression is $\cos 62-\sin 28$

Step 2. Convert into the same trigonometrical ratio

The given expression is $\cos 62-\sin 28$

Here, $\cos \left(90-\theta \right)=\sin \left(\theta \right)$

Therefore,role="math" localid="1646652714529" $$\begin{gathered} =\cos \left(62\right)-\sin \left(28\right) \\ =\cos (90-28)-\sin \left(28\right) \\ =\sin \left(28\right)-\sin \left(28\right) \\ =0 \end{gathered}$$

Step 3. Conclusion

Hence, the simplified value is$0$