Question

if cosecA=8/5, find the value of sec(90-A)



please answer fast
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Answer 1

Let theta = A, for simplicity in solution.

Numerator 

= Sec A cosec(90-A)  - Tan A Cot(90 - A) + sin² 55 + sin² 35

= Sec A * sec A - tan A * tan A + sin² 55 + Cos² (90-35)

= 1 + 1

= 2

as  sin²A + cos²A = 1  for any angle A.

sec²A - tan²A = 1   for any angle

cosec(90-A) = sec A

cot (90-A) = tan A

=====

we know  that    tan A = cot (90-A) = 1 / tan (90-A) .    Let us apply this

Denominator

= tan 10 tan 80 tan 60 tan 20 tan 70

= tan 10 * 1/tan10 * tan 60 * tan 20 * 1/tan20

= tan 60

= √3

Answer = 2/√3