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Mathematics
Mathematics
Problem
For an acute angle
β
\beta
β
, it is given that
sin
(
90
∘
−
β
)
=
5
13
\sin(90^{\circ}-\beta)=\dfrac{5}{13}
sin
(
9
0
∘
−
β
)
=
13
5
. a. (i) Find the exact value of
tan
β
\tan \beta
tan
β
. b. (ii) Hence evaluate
cot
(
90
∘
−
β
)
sec
β
\dfrac{\cot(90^{\circ}-\beta)}{\sec \beta}
sec
β
cot
(
9
0
∘
−
β
)
and express your answer as a rational number.
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