A Without using trigonometric tables evaluate-sin 35-cos 55-cos 35-sin 55-cosec2 10-tan 2 80-b Evaluate without using trigonometric tables-cos 2 26-cos 64-sin 26-tan 36- 54- -6 MARKS-

Each Part: 3 Marks (a) =sin 35^∘ cos 55^∘ + cos 35^∘ sin 55^∘/cosec^2 10^∘ tan^2 80^∘ =sin 35^∘ cos(90 35^∘)+cos 35^∘ sin(90^∘ 35^∘)/cosec^2 10^∘ tan^2( ...

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Byju's Answer

Standard X

Mathematics

Relation between Trigonometric Ratios

a Without usi...

Question

(a) Without using trigonometric tables evaluate:
$\frac{s i n 35^{\circ} c o s 55^{\circ} + c o s 35^{\circ} s i n 55^{\circ}}{c o s e c^{2} 10^{\circ} - t a n^{2} 80^{\circ}}$

(b) Evaluate without using trigonometric tables:
$c o s^{2} 26^{\circ} + c o s 64^{\circ} s i n 26^{\circ} + \frac{t a n 36^{\circ}}{c o t 54^{\circ}}$ [6 MARKS]

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Solution

Each Part: 3 Marks

(a) $= \frac{s i n 35^{\circ} c o s 55^{\circ} + c o s 35^{\circ} s i n 55^{\circ}}{c o s e c^{2} 10^{\circ} - t a n^{2} 80^{\circ}}$

$= \frac{s i n 35^{\circ} c o s (90 - 35^{\circ}) + c o s 35^{\circ} s i n (90^{\circ} - 35^{\circ})}{c o s e c^{2} 10^{\circ} - t a n^{2} (90^{\circ} - 10^{\circ})}$

$= \frac{s i n 35^{\circ} . s i n 35^{\circ} + c o s 35^{\circ} . c o s 35^{\circ}}{c o s e c^{2} 10^{\circ} - c o t^{2} 10^{\circ}}$

$= \frac{s i n^{2} 35^{\circ} + c o s^{2} 35^{\circ}}{1} = \frac{1}{1} = 1$

(b) $c o s^{2} 26^{\circ} + c o s (90^{\circ} - 26^{\circ}) s i n 26^{\circ} + \frac{t a n 36^{\circ}}{t a n 36^{\circ}}$

$= c o s^{2} 26^{\circ} + s i n 26^{\circ} s i n 26^{\circ} + \frac{t a n 36^{\circ}}{t a n 36^{\circ}}$

$= c o s^{2} 26^{\circ} + s i n^{2} 26^{\circ} + 1 = 1 + 1 = 2$

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Similar questions

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(a) Without using trigonometric tables evaluate: sin 35∘ cos 55∘+cos 35∘ sin 55∘cosec2 10∘−tan2 80∘ (b) Evaluate without using trigonometric tables: cos2 26∘+cos 64∘ sin 26∘+tan 36∘cot 54∘ [6 MARKS]