Express each of the following in trigonometric ratios of angles between $0^{\circ} a n d 45^{\circ}$ :
$s i n 85^{\circ} + c o s e c 85^{\circ}$

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Solution

We have,

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

$= s i n (90^{\circ} - 5^{\circ}) + c o s e c (90^{\circ} - 5^{\circ})$

$= c o s 5^{\circ} + s e c 5^{\circ}$ $[∵ s i n (90^{\circ} - θ) = c o s θ a n d c o s e c (90^{\circ} - θ) = s e c θ]$

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

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tan 81^{\circ} + cos 72^{\circ}

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cot 85^{\circ} + cos 75^{\circ}

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tan 65^{0} + cot 49^{0}

cosec 54^{0} + sin 72^{0}

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