Question

secA + tan A then the quadrants in which the angles A lies are
1 + sin A
If
V1-sin A
20.
B) II, III
C) I only
A) I, II
D) III, IV​

Answer 1

Answer:

Correct option is

C

I,IV

1−sinA1+sinA=(1−sinA)(1+sinA)(1+sinA)(1+sinA)=1−sin2A(1+sinA)2=cos2A(1+sinA)2=(cosA1+sinA)2=(secA+tanA)2

Given 1−sinA1+sinA=secA+tanA

⟹∣secA+tanA∣=secA+tanA

So ⟹secA+tanA≥0⟹(1+sinA)cosA≥0⟹cosA≥0    (∵1+sinA∈[0,2])

So A lies in first and fourth quadrants