2 tan 70- 20-tan 33- 57-2cos 45-

The correct option is A 0 2 tan 70^∘/cot 20^∘ tan 33^∘/cot 57^∘ √(2) cos 45^∘ =2 tan (90 20^∘)/cot 20 tan (90 57^∘)/cot 57^∘ √(2)(1/√(2) ) = 2 cot 20^ ...

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Byju's Answer

Standard IX

Mathematics

Values of Trigonometric Ratios

2 tan 70∘/ 20...

Question

$2 \frac{t a n 70^{\circ}}{c o t 20^{\circ}} - \frac{t a n 33^{\circ}}{c o t 57^{\circ}} - \sqrt{2} c o s 45^{\circ} =$ _____

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Solution

The correct option is A
0

$2 \frac{t a n 70^{\circ}}{c o t 20^{\circ}} - \frac{t a n 33^{\circ}}{c o t 57^{\circ}} - \sqrt{2} c o s 45^{\circ}$

$= 2 \frac{t a n (90 - 20^{\circ})}{c o t 20} - \frac{t a n (90 - 57^{\circ})}{c o t 57^{\circ}} - \sqrt{2} (\frac{1}{\sqrt{2}})$
$= 2 \frac{c o t 20^{\circ}}{c o t 20^{\circ}} - \frac{c o t 57^{\circ}}{c o t 57^{\circ}} - 1$ $(∵ t a n (90 - θ) = c o t θ)$
= 2 - 1 - 1
= 0

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2 tan 70∘cot 20∘−tan 33∘cot 57∘−√2 cos 45∘= _____

The correct option is A 0 2 tan 70∘cot 20∘−tan 33∘cot 57∘−√2 cos 45∘ =2 tan (90−20∘)cot 20−tan (90−57∘)cot 57∘−√2(1√2) =2 cot 20∘cot 20∘−cot 57∘cot 57∘−1(∵ tan(90−θ)=cot θ) = 2 - 1 - 1 = 0

$2 \frac{t a n 70^{\circ}}{c o t 20^{\circ}} - \frac{t a n 33^{\circ}}{c o t 57^{\circ}} - \sqrt{2} c o s 45^{\circ} =$ _____