cos 60°
sin 60°
tan 60°
sin 30°
\(\frac{2\ tan\ 30°}{1 - tan^2 30°}\)
\(=\frac{ 2 × \left(\frac{1}{\sqrt3}\right) }{ 1 - \left(\frac{1}{\sqrt3}\right)^2}\)
\(= \frac{\left(\frac{2}{\sqrt3}\right) }{ \left(1 - \frac{1}{3}\right)}\)
\(= \frac{\left(\frac{2}{\sqrt3}\right) }{ \left(\frac{2}{3}\right)}\)
\(= \sqrt3\)
The expression equals \( \sqrt3 \). Among the given options, only tan 60° equals \( \sqrt3 \).
Therefore, option (C) is correct.
Evaluate the following.
(i) sin60° cos30° + sin30° cos 60°
(ii) 2tan245° + cos230° - sin260°
(iii) \(\frac{cos 45°}{sec 30°+cosec30°}\)
(iv) \(\frac{sin\ 30°+tan\ 45°cosec\ 60°}{sec\ 30°+cos\ 60°+cot\ 45°}\)
(v) \(\frac{5cos^260°+4sec^230°-tan^245°}{sin^230°+cos^230°}\)