Without using a calculator, express each of the following in exact form. $\sin 105^\circ$ \(\tan 1

Question

Without using a calculator, express each of the following in exact form. $\sin 105^\circ$ $\tan 15^\circ$ $\sec 285^\circ$ $\cos 75^\circ$ $\cot 195^\circ$ $\operatorname{cosec} 165^\circ$

Accepted Answer

(i) $\dfrac{\sqrt{6}+\sqrt{2}}{4}$; (ii) $\dfrac{\sqrt{6}-\sqrt{2}}{4}$; (iii) $2-\sqrt{3}$; (iv) $2+\sqrt{3}$; (v) $\sqrt{6}+\sqrt{2}$; (vi) $\sqrt{6}+\sqrt{2}$

Trigonometry - Compound and Double-Angle Identities

Trigonometry - Compound and Double-Angle Identities

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