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Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios] — MATHEMATICS STD 9 — Question

ICSE BoardEnglish MediumSTD 9MATHEMATICSTrigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]2 Marks
Question
Calculate the value of $A,$ if $( \operatorname{cosec} 2A - 2) (\cot 3A - 1) = 0$
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Answer

$( \operatorname{cosec}  2A – 2) (\cot 3A – 1) = 0$
$ \operatorname{cosec}  2A – 2 = 0$ and $\cot 3A – 1 = 0$
$ \ ( \operatorname{cosec}  2A = 2$ and $\cot 3A = 1$
$ \operatorname{cosec}  2A = \operatorname{cosec}\  30^\circ $ and $\cot 3A = \cot 45^\circ $
$2A = 30^\circ $ and 3$A = 45^\circ $
$A = 15^\circ $ and $A = 15^\circ $

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