Question

11. Show that
1 + sin A
Vi sin
= sec A+ tan A​

Answer 1

LHS=
1−sinA
1+sinA
​

​


=
1−sinA
1+sinA
​
×
1+sinA
1+sinA
​

​


=
(1+sinA)(1−sinA)
(1+sinA)
2

​

​


=
1−sin
2
A
(1+sinA)
2

​

​


=
cos
2
A
(1+sinA)
2

​

​


=
(
cosA
1+sinA
​
)
2

​


=
cosA
1+sinA
​


=
cosA
1
​
+
cosA
sinA
​


=secA+tanA

=RHS



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