If 2sec
2
A=x, then the value of x is:
- A1+cosA
1
+
1−cosA
1
- B1+tanA
1
+
1−sinA
1
- C1+sinA
1
+
1−sinA
1
- D1+cotA
1
+
1−cosA
1
Solution & Step-by-step Explanation
Let's simplify Option C:
1+sinA
1
+
1−sinA
1
Take the common denominator:
=
(1+sinA)(1−sinA)
(1−sinA)+(1+sinA)
=
1−sin
2
A
2
Since 1−sin
2
A=cos
2
A:
=
cos
2
A
2
=2sec
2
A
This perfectly matches the given expression x=2sec
2
A.
1+sinA
1
+
1−sinA
1
Take the common denominator:
=
(1+sinA)(1−sinA)
(1−sinA)+(1+sinA)
=
1−sin
2
A
2
Since 1−sin
2
A=cos
2
A:
=
cos
2
A
2
=2sec
2
A
This perfectly matches the given expression x=2sec
2
A.