Calculate the value of $A$ (A is acute angle),in degrees if
$(t a n A - 1) (c o s e c 3 A - 1) = 0$
What is the smaller value of the angle $A$ (in degrees)?

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Solution

$(tan A - 1) (c o s e c 3 A - 1) = 0$
Either $tan A - 1 = 0$ or $c o s e c 3 A - 1 = 0$
Either $t a n A = 1$ or $c o s e c 3 A = 1$
$t a n A = tan 45$ or $3 A = 90$
$A = 45^{\circ}$ or $A = 30^{\circ}$
Thus the smaller value of $A$ in degrees is $30$

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