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Without using trigonometric tables, eval...

Without using trigonometric tables, evaluate :
(i) `(cos 53^@)/(sin 37^@)`
(ii) ` (tan68^@)/(cot 22^@)`
(iii)`(sec49^@)/(cosec 41^@)`
(iv) `(sin 30^@17')/(cos 59^@43')`

Text Solution

Verified by Experts

(i) `(cos 53^@)/(sin 37^@) =(cos(90^@-37^@))/(sin 37^@)= (sin37^@)/(sin37^@)=1 [because cos (90^@-theta)=sin theta]`.
(ii) ` (tan68^@)/(cot 22^@)=(tan (90^@-22^@))/(cot 22^@)=(cot 22^@)/(cot 22^@)=(cot22^@)/(cot 22^@)=1 [because cos (90^@-theta) =cot theta]`
(iii)`(sec49^@)/(cosec 41^@)=(sec(90^@-41^@))/(cossec 41^@)=(cosec 41^@)/(cosec41^@)=1 [because sec (90^@-theta) =cosec theta]`.
(iv) `(sin 30^@17')/(cos 59^@43')=(sin [90^@-(59-43')])/(cos 59^@43')=(cos 59^@43')/(cos 59^@43')=1`.
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