If A cos 12 deg minus cos 36 deg sin 96 deg sin 24 deg and B sin 60 deg minus sin 12 deg cos 48 deg ...........

Mathematics (NDA) Trigonometry

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If A = (cos 12° − cos 36° ) (sin 96° + sin 24° ) and B = (sin 60° − sin 12° ) (cos 48° − cos 72° ), then what is

A/B equal to?

-1

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Explanation:

We have, A = (cos 12° − cos 36° ) (sin 96° + sin 24° )
and B = (sin 60° − sin 12° ) (cos 48° − cos 72° )
Now, consider
A = (cos 12° − cos 36° ) (sin 96° + sin 24° )
= − 2 sin 24° sin (−12° ) (2 sin 60° cos 36° )
= 4 sin 24° sin 12° sin 60° cos 36°
and B = 2 cos 36° sin 24° (−2 sin 60° sin (−12° ))
= 4 sin 24° sin 12° sin 60° cos 36°
Clearly, A/B= 1