Solve \[\sec 2A=2\].

Hint: In this problem, we have to solve and find the value of A. We can first find the angle whose value is equal to 2. We can then divide 2 on both sides to get the value of A. we know that \[\cos x=\dfrac{1}{\sec x}\], we also know that when \[\cos x=\dfrac{1}{2}\], then the value of \[x=\dfrac{\pi }{3}\]. Similarly, we can see that when \[\sec x=2\], then the value of \[x=\dfrac{\pi }{3}\]. We can then substitute the value in the given expression and simplify it to get the value of A.

Complete step by step solution:
Here we have to solve \[\sec 2A=2\] and find the value of A.
We know that \[\cos x=\dfrac{1}{\sec x}\].
We know that when \[\cos x=\dfrac{1}{2}\], then the value of \[x=\dfrac{\pi }{3}\]
Similarly, we can see that when \[\sec x=2\], then the value of \[x=\dfrac{\pi }{3}\].
We can now write the given expression by substituting the above value, we get
 \[\Rightarrow 2A=\dfrac{\pi }{3}\]
We can now divide 2 on both sides in the above step, we get
\[\Rightarrow A=\dfrac{\pi }{6}={{30}^{\circ }}\]
Therefore, the value of \[A={{30}^{\circ }}\].

Note: We should remember that we should know the trigonometric degree values to solve these types of problems. We should know that solve is nothing but finding the unknown value of the given expression. We should know that when \[\cos x=\dfrac{1}{2}\], then the value of \[x=\dfrac{\pi }{3}\]. Similarly, we can see that when \[\sec x=2\], then the value of \[x=\dfrac{\pi }{3}\]. We can also write the general equation format to find every value of A.