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Mathematics Question on Trigonometric Functions

log⁡(tan⁡18∘)+log⁡(tan⁡36∘)+log⁡(tan⁡54∘)+log⁡(tan⁡72∘)=\log ( \tan 18\degree) + \log ( \tan 36\degree) + \log ( \tan 54\degree) + \log (\tan 72\degree) =

A

log⁡4\log 4

B

log⁡3\log 3

C

log⁡2\log 2

D

0

Answer

0

Explanation

Solution

log⁡(tan⁡18?tan⁡36?tan⁡54?tan⁡72?)=log⁡1\log ( \tan 18? \tan 36? \tan 54? \tan 72?) = \log 1 [∵  IfA+B=90∘ ⇒ tan⁡ A tan⁡ B=1][\because \:\:If A+ B = 90^\circ \, \Rightarrow \, \tan \, A \, \tan \, B = 1]