Given interval is `[0,2pi]` . And given identity is `secx+tanx=1` which we can write as `1/(cosx)+(sinx)/(cosx)=1` `or` , `(1+sinx)/(cosx)=1` or, `(1+sinx)=cosx` or, `1+sinx-cosx=0` or, `1+2sin(x/2)cos(x/2)-(1-2sin^2(x/2))=0` or, `1+2sin(x/2)cos(x/2)-1+2sin^2(x/2)=0` or, `2sin(x/2)cos(x/2)+2sin^2(x/2)=0` or, `2sin(x/2)[cos(x/2)+sin(x/2)]=0` `or,` `2sin(x/2)=0` and `cos(x/2)+sin(x/2)=0` . Now, `2sin(x/2)=0` `rArrsin(x/2)=0` `rArrsin(x/2)=sin(npi)` , n=0,1,2. As per the need of our problem. `rArr x/2=npi` or, `x=2npi` for n=0,1 as our interval is `[0,2pi]` . So, `x=0` or, `x=2pi` . Now, if `cos(x/2)+sin(x/2)=0` `rArr1+(sin(x/2))/cos(x/2)=0` `rArrtan(x/2)=-1` or, `tan(x/2)=tan(pi/2+pi/4)` or, `x/2=(pi/2+pi/4)` or, `x=pi+pi/2` or, `x=3pi/2` . Clearly, `x=0` and `x=2pi` are the solutions satisfying our given identity over the given interval. Solution Given interval is `[0,2pi]` . And given identity is `secx+tanx=1` which we can write as `1/(cosx)+(sinx)/(cosx)=1` `or` , `(1+sinx)/(cosx)=1` or, `(1+sinx)=cosx` or, `1+sinx-cosx=0` or, `1+2sin(x/2)cos(x/2)-(1-2sin^2(x/2))=0` or, `1+2sin(x/2)cos(x/2)-1+2sin^2(x/2)=0` or, `2sin(x/2)cos(x/2)+2sin^2(x/2)=0` or, `2sin(x/2)[cos(x/2)+sin(x/2)]=0` `or,` `2sin(x/2)=0` and `cos(x/2)+sin(x/2)=0` . Now, `2sin(x/2)=0` `rArrsin(x/2)=0` `rArrsin(x/2)=sin(npi)` , n=0,1,2. As per the need of our problem. `rArr x/2=npi` or, `x=2npi` for n=0,1 as our interval is `[0,2pi]` . So, `x=0` or, `x=2pi` . Now, if `cos(x/2)+sin(x/2)=0` `rArr1+(sin(x/2))/cos(x/2)=0` `rArrtan(x/2)=-1` or, `tan(x/2)=tan(pi/2+pi/4)` or, `x/2=(pi/2+pi/4)` or, `x=pi+pi/2` or, `x=3pi/2` . Clearly, `x=0` and `x=2pi` are the solutions satisfying our given identity over the given interval..

1. public class Deque {
private class Node {
public int data;
public Node leftNode;
public Node rightNode;
private Node(int data) {
this.data = data;
leftNode = null;
rightNode = null;
}
private Node(int data, null, Node rightNode) {
this.data = data;
this.leftNode = null;
this.rightNode = rightNode;
}
private Node(int data, Node leftNode, null) {
this.data = data;
this.leftNode = leftNode;
this.rightNode = null;
}
private Node(int data, Node leftNode, Node rightNode) {
this.data = data;
this.leftNode = leftNode;
this.rightNode = rightNode;
}
}
private Node leftEnd = null;
private Node rightEnd = null;
public Deque() {
}
public void InsertLeft(int data) {
if ((leftEnd == null) && (rightEnd == null)) {
Node item = new Node(data);
leftEnd = item;
rightEnd = item;

2. } else {
Node item = new Node(data, leftEnd, null);
leftEnd.leftNode = item;
leftEnd = item;
}
}
public int DeleteRight() {
int temp = rightEnd.data;
rightEnd = rightEnd.leftNode;
rightEnd.rightNode = null;
return temp;
}
}
public class Deque {
private class Node {
public int data;
public Node leftNode;
public Node rightNode;
private Node(int data) {
this.data = data;
leftNode = null;
rightNode = null;
}
private Node(int data, Node leftNode, Node rightNode) {
this.data = data;
this.leftNode = leftNode;
this.rightNode = rightNode;
}
}
private Node header = new Node(0);
public Deque() {
}
public void InsertLeft(int data) {
if (header.data == 0) {
Node item = new Node(data);
item.leftNode = item;

3. item.rightNode = item;
header.leftNode = item;
header.rightNode = item;
} else {
Node item = new Node(data, header.leftNode, header.rightNode);
Node old_leftEnd = header.leftNode;
old_leftEnd.rightNode = item;
Node rightEnd = header.rightNode;
temp.leftNode = item;
header.leftNode = item;
}
header.data++;
}
public Node DeleteRight() {
if (header.data == 0 ) {
} else {
Node old_rightEnd = header.rightNode; Node leftEnd = header.leftNode; // reference to leftEnd
Node new_rightEnd = old_rightEnd.rightNode; /* link new rightEnd to leftEnd */
new_rightEnd.leftNode = leftEnd;
leftEnd.rightNode = new_rightEnd;
header.rightNode = new_rightEnd;
}
header.data--;
}
Solution
public class Deque {
private class Node {
public int data;
public Node leftNode;
public Node rightNode;
private Node(int data) {
this.data = data;
leftNode = null;
rightNode = null;

4. }
private Node(int data, null, Node rightNode) {
this.data = data;
this.leftNode = null;
this.rightNode = rightNode;
}
private Node(int data, Node leftNode, null) {
this.data = data;
this.leftNode = leftNode;
this.rightNode = null;
}
private Node(int data, Node leftNode, Node rightNode) {
this.data = data;
this.leftNode = leftNode;
this.rightNode = rightNode;
}
}
private Node leftEnd = null;
private Node rightEnd = null;
public Deque() {
}
public void InsertLeft(int data) {
if ((leftEnd == null) && (rightEnd == null)) {
Node item = new Node(data);
leftEnd = item;
rightEnd = item;
} else {
Node item = new Node(data, leftEnd, null);
leftEnd.leftNode = item;
leftEnd = item;
}
}
public int DeleteRight() {
int temp = rightEnd.data;
rightEnd = rightEnd.leftNode;
rightEnd.rightNode = null;

5. return temp;
}
}
public class Deque {
private class Node {
public int data;
public Node leftNode;
public Node rightNode;
private Node(int data) {
this.data = data;
leftNode = null;
rightNode = null;
}
private Node(int data, Node leftNode, Node rightNode) {
this.data = data;
this.leftNode = leftNode;
this.rightNode = rightNode;
}
}
private Node header = new Node(0);
public Deque() {
}
public void InsertLeft(int data) {
if (header.data == 0) {
Node item = new Node(data);
item.leftNode = item;
item.rightNode = item;
header.leftNode = item;
header.rightNode = item;
} else {
Node item = new Node(data, header.leftNode, header.rightNode);
Node old_leftEnd = header.leftNode;
old_leftEnd.rightNode = item;
Node rightEnd = header.rightNode;
temp.leftNode = item;
header.leftNode = item;

6. }
header.data++;
}
public Node DeleteRight() {
if (header.data == 0 ) {
} else {
Node old_rightEnd = header.rightNode; Node leftEnd = header.leftNode; // reference to leftEnd
Node new_rightEnd = old_rightEnd.rightNode; /* link new rightEnd to leftEnd */
new_rightEnd.leftNode = leftEnd;
leftEnd.rightNode = new_rightEnd;
header.rightNode = new_rightEnd;
}
header.data--;
}