Question

17. If sec 5A = cosec (A + 30) where 5A is an acute angle then value of
A is.
(a) 15° (b) 5
(c) 20°
(d) 10°​

Answer 1

Given

sec 5A = cosec ( A + 30 )

{ we know secA = cosec (90 – A) }

cosec ( 90 – 5A ) = cosec ( A + 30 )

Since cosec of both the angles are same therefore angles will also be same

➡ 90 – 5A = A + 30

➡ – 6A = 30 – 90

➡ – 6A = – 60

➡ A = 60 / 6

➡ A = 10

Hence, (d) 10° is the correct answer