How to find tan 53 without remembering any values like cos 37 or sin 37

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Q. The value of

\frac{{sin}^{2} 53 + {cos}^{2} 53}{{sec}^{2} 37 - {tan}^{2} 37}

Q. Find the value of

\frac{s i n 35^{0}}{c o s 55^{0}} + \frac{t a n 37^{0}}{c o t 53^{0}}

Q. Value of

s i n 37 ° . c o s 53 °

Without using tables, evaluate:
(i) sin $53^{\circ} \div c o s 37^{\circ}$
(ii) cos $49^{\circ} \div s i n 41^{\circ}$
(iii) tan $66^{\circ} \div c o t 24^{\circ}$

Q. The value of sin (

37^{0}

)

\times

cos (

53^{0}

) =

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