Question

prove that log tan1 + log tan2+......+log tan 89 = 0

Answer 1

Heya User,

--> Rules used --> log a + log b = log [ a * b ]
                          --> tan a * tan ( 90 - a ) = 1

Now, ATQ --> 

--> log tan(1) + log tan(2) + ... + log tan(89) 
               = log ( tan(1) * tan(2) * ... * tan(89) )
               = log [ ( tan 1 * tan 89 ) ... ( tan 44 * 46 ) * tan 45 ]
               = log [ 1 * 1 * 1 * 1 * .... * 1 ]  ----> [ tan 45 = 1 ]
               = log 1 = 0 

Hence, proved ^_^