Express each of the following in trigonometric ratios of angles between $0^{\circ} a n d 45^{\circ}$ :
$s i n 72^{\circ} + c o t 72^{\circ}$

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Solution

$s i n 72^{\circ} + c o t 72^{\circ}$

$= s i n (90^{\circ} - 18^{\circ}) + c o t (90^{\circ} - 18^{\circ})$

$= c o s 18^{\circ} + t a n 18^{\circ}$

$[∵ s i n (90^{\circ} - 18^{\circ}) = c o s 18^{\circ}, c o t (90^{\circ} - 18^{\circ}) = t a n 18^{\circ}]$

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Express each of the following in trigonometric ratios of angles between 0∘and45∘ :sin72∘+cot72∘

sin72∘+cot72∘=sin(90∘−18∘)+cot(90∘−18∘)=cos18∘+tan18∘[∵sin(90∘−18∘)=cos18∘,cot(90∘−18∘)=tan18∘]

Express each of the following in trigonometric ratios of angles between $0^{\circ} a n d 45^{\circ}$ :
$s i n 72^{\circ} + c o t 72^{\circ}$

$s i n 72^{\circ} + c o t 72^{\circ}$

$= s i n (90^{\circ} - 18^{\circ}) + c o t (90^{\circ} - 18^{\circ})$

$= c o s 18^{\circ} + t a n 18^{\circ}$

$[∵ s i n (90^{\circ} - 18^{\circ}) = c o s 18^{\circ}, c o t (90^{\circ} - 18^{\circ}) = t a n 18^{\circ}]$