Question

If sec 5A=cosec (A-30), where 5 A is an acute angle, then find value of A.

Answer 1

Sec 5A = cosec (A-30)
A < 90 deg.

we know cosec B = sec(90-B) 
so   cosec(A - 30) = sec(90 - (A-30))
 so  sec (120-A)  =  sec (5A)

so   either  120 - A = 5A       or    120 - A  = - 5A
so               A = 20°    or   -30° or 330°

Answer 2

Step-by-step explanation:

sec5A=sec(90°-A+30°)

property used

(sec 30=cos 60 )

(sec30=sec(90-30))

5A= 120°-A

6A=120°

therefore

A= 20°