Question

In √1+sin A /1-sin A = sec A + tan A, Prove RHS=LHS.​

Answer 1

Step-by-step explanation:

1−sinA1+sinA=(1−sinA)(1−sinA)(1+sinA)(1−sinA)

=(1−sinA)21−sin2A

=(1−2sinA+sin2A)cos2A

=(1cos2A−2sinAcos2A+sin2Acos2A)

=(sec2A−2.1cosA.sinAcosA+tan2A)

=(sec2A−2secA.tanA+tan2A)

=(secA−tanA)2

Hence proved.

Note: The question should be (1−sinA1+sinA)=(secA−tanA)2