sin 60°
cos 60°
tan 60°
sin 30°
sin 30°
\(= \frac{2 × \left(\frac{1}{\sqrt3}\right)}{1 + \left(\frac{1}{\sqrt3}\right)^2}\)
\(=\frac{ 2 × \left(\frac{1}{\sqrt3}\right)}{(1 + \frac{1}{3})}\)
\(= \frac{\frac{2}{\sqrt3} }{ \frac{4}{3}}\)
\(=\frac{ 6}{4\sqrt3}\)
\(= \frac{\sqrt3}{2}\)
Of the given options, sin 60° \(= \frac{\sqrt3}{2}\) is the correct answer.
Therefore, (A) 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) \(\frac{5cos^260°+4sec^230°-tan^245°}{sin^230°+cos^230°}\)