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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
find the value of $: \cos^2 60^\circ+ \sec^2 30^\circ+ \tan^2 45^\circ$
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Answer

$\cos^2 60^\circ + \sec^2 30^\circ + \tan^2 45^\circ$
$=\left(\frac{1}{2}\right)^2+\left(\frac{2}{\sqrt{3}}\right)^2+1^2$
$=\frac{1}{4}+\frac{4}{3}+1$
$=\frac{3+16+12}{12}$
$=\frac{31}{12}$
$=2 \frac{7}{12}$

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