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T-Ratios of Some Particular Angles — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsT-Ratios of Some Particular Angles2 Marks
Question
Evaluate the following:
$\frac{\sin30^\circ}{\cos45^\circ}+\frac{\cot45^\circ}{\sec60^\circ}-\frac{\sin60^\circ}{\tan45^\circ}+\frac{\cos30^\circ}{\sin90^\circ}$
✓

Answer

$\frac{\sin30^\circ}{\cos45^\circ}+\frac{\cot45^\circ}{\sec60^\circ}-\frac{\sin60^\circ}{\tan45^\circ}+\frac{\cos30^\circ}{\sin90^\circ}$
$=\frac{\big(\frac14\big)}{\big(\frac{1}{\sqrt{2}}\big)}+\frac12-\frac{\Big(\frac{\sqrt{3}}{2}\Big)}{1}+\frac{\Big(\frac{\sqrt{3}}{2}\Big)}{1}$
$=\frac{\sqrt{2}}{2}+\frac12-\frac{{\sqrt{3}}}{2}+\frac{\sqrt{3}}{2}$
$=\frac{\sqrt{2}+1}{2}$

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