What is the value of -sin 18-cos 72-1-1-1-2-0-

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Complementary Trigonometric ratios

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What is the value of (sin 18°)/(cos 72°)?

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Without using trigonometric tables, prove that:

(i) $s i n 53^{\circ} c o s 37^{\circ} + c o s 53^{\circ} s i n 37^{\circ} = 1$

(ii) $c o s 54^{\circ} c o s 36^{\circ} - s i n 54^{\circ} s i n 36^{\circ} = 0$

(iii) $s e c 70^{\circ} s i n 20^{\circ} + c o s 20^{\circ} c o s e c 70^{\circ} = 2$

(iv) $s i n 35^{\circ} s i n 55^{\circ} - c o s 35^{\circ} c o s 55^{\circ} = 0$

(v) $(s i n 72^{\circ} + c o s 18^{\circ}) (s i n 72^{\circ} - c o s 18^{\circ}) = 0$

(vi) $t a n 48^{\circ} t a n 23^{\circ} t a n 42^{\circ} t a n 67^{\circ} = 1$

(\cos \frac{2 π}{3}) + \sin^{- 1} (\sin \frac{2 π}{3})

{sin}^{2} 18^{0} - {cos}^{2} 72^{0}

What is the value of (sin 18°)/(cos 72°)?

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