Question

If sec A= cosec( A-27), where 2A is an acute angle ,find measure of<A

Answer 1

secA=cosec(A-27)
cosec(90-A)=cosec(A-27)              {complementary angles}
90-A=cosec(A-27)
              cosec
90-A=A-27
90+27=A+A
2A=117
A=117
      2
A=58.5
A=59 (approximately)

Answer 2

Change sec A in cosec (90 -A) = cosec (A-27)
Cosec cross with cosec
Then we have,
(90-A) = (A-27)
90+27=A+A
117=2A
A=117/2