Without using trigonometrical tables- find the value of cos 2 20-cos 2 70-sin 2 59-sin 2 31- -3 MARKS-

Formula: 1 Mark Solution: 2 Marks cos^220^∘+cos^270^∘/sin^259^∘+sin^231^∘=cos^220^∘+sin^2(90^∘ 70^∘)/cos^2(90^∘ 59^∘)+sin^231^∘ =cos^220^∘+sin^220^∘/cos^231^∘ ...

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Standard X

Mathematics

Trigonometric Ratios

Without using...

Question

Without using trigonometrical tables, find the value of $\frac{c o s^{2} 20^{\circ} + c o s^{2} 70^{\circ}}{s i n^{2} 59^{\circ} + s i n^{2} 31^{\circ}}$ [3 MARKS]

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Solution

Formula: 1 Mark
Solution: 2 Marks

$\frac{c o s^{2} 20^{\circ} + c o s^{2} 70^{\circ}}{s i n^{2} 59^{\circ} + s i n^{2} 31^{\circ}} = \frac{c o s^{2} 20^{\circ} + s i n^{2} (90^{\circ} - 70^{\circ})}{c o s^{2} (90^{\circ} - 59^{\circ}) + s i n^{2} 31^{\circ}} = \frac{c o s^{2} 20^{\circ} + s i n^{2} 20^{\circ}}{c o s^{2} 31^{\circ} + s i n^{2} 31^{\circ}} = \frac{1}{1} = 1$

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Without using trigonometrical tables, find the value of cos220∘+cos270∘sin259∘+sin231∘ [3 MARKS]

Formula: 1 Mark Solution: 2 Marks cos220∘+cos270∘sin259∘+sin231∘=cos220∘+sin2(90∘−70∘)cos2(90∘−59∘)+sin231∘=cos220∘+sin220∘cos231∘+sin231∘=11=1

Without using trigonometrical tables, find the value of $\frac{c o s^{2} 20^{\circ} + c o s^{2} 70^{\circ}}{s i n^{2} 59^{\circ} + s i n^{2} 31^{\circ}}$ [3 MARKS]