sec(a+15)=csc(2a)

Find the smallest possible value of a.
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1 Answer

csc(90−x) = sec(x)
sec(a+15) = csc(2a)
csc(90−a−15) = csc(2a)
csc(75−a) = csc(2a)
sin(75−a) = sin(2a)
2a = 75 − a + 360k, for all integers k
3a = 75 + 360k
a = 25 + 120k
a = 25 (smallest positive value)
2a = 180 − (75−a) + 360k
2a = 105 + a + 360k
a = 105 + 360k
a = 105 (smallest positive value)
a = 25

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