The trigonometric ratio equivalent to the following is:

$s i n 55^{\circ} + c o s 20^{\circ} + c o t 70^{\circ} + c o s e c 85^{\circ}$

$c o s 35^{\circ} + s i n 20^{\circ} + t a n 20^{\circ} + s e c 5^{\circ}$

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$c o s 35^{\circ} + s i n 70^{\circ} + t a n 20^{\circ} + s e c 5^{\circ}$

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$c o s 35^{\circ} + s i n 20^{\circ} + t a n 70^{\circ} + s e c 5^{\circ}$

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$c o s 35^{\circ} + s i n 20^{\circ} + t a n 70^{\circ} + s e c 85^{\circ}$

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Solution

The correct option is B
$c o s 35^{\circ} + s i n 70^{\circ} + t a n 20^{\circ} + s e c 5^{\circ}$

Since,

$s i n A = c o s (90^{\circ} - A)$

$c o s A = s i n (90^{\circ} - A)$

$c o s e c A = s e c (90^{\circ} - A)$

$c o t A = t a n (90^{\circ} - A)$

$H e n c e, s i n 55^{\circ} + c o s 20^{\circ} + c o t 70^{\circ} + c o s e c 85^{\circ} = c o s (90^{\circ} - 35^{\circ}) + s i n (90^{\circ} - 70^{\circ}) + t a n (90^{\circ} - 20^{\circ}) + s e c (90^{\circ} - 5^{\circ}) = c o s 35^{\circ} + s i n 70^{\circ} + t a n 20^{\circ} + s e c 5^{\circ}$

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Similar questions

Find the trigonometric ratio equivalent to the following:

$s i n 55^{\circ} + c o s 20^{\circ} + c o t 70^{\circ} + c o s e c 85^{\circ}$

0^{\circ} a n d 45^{\circ}

s i n 85^{\circ} + c o s e c 85^{\circ}

Express (sin $85^{\circ}$ + cosec $85^{\circ}$ ) in terms of trigonometric ratios of angles between $0^{\circ}$ and $45^{\circ}$ .

cosec

^{o}

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