\sqrt { \frac { 1 + \sin A } { 1 - \sin A } } = \sec A + \tan A
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1−sinA
1+sinA
=secA+tanA
Medium
Solution
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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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