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Find the value of tan22 1/2.

Asked by SIVENDU SIVENDU 28th July 2012, 5:39 PM
Answered by Expert
Answer:
Answer : To find the value of tan 22.5 degree
 
we know that [ ( 1- cos 2x ) / ( 1+ cos 2x) ] = tan2
 
therefore
=> tan 22.5  = square root  ( tan2 22.5) 
=> square root [ (1 - cos 45 ) / (1+ cos 45) ]
=> square root [ ( 1- (1/ square root 2) ) / ( 1 + (1/ square root 2) ) ]
 => squareroot [  ( ( squareroot 2) - 1 ) /  ( (squareroot 2) + 1 ) ]
 
Now rationalising by  ((squareroot 2) - 1 ) , we get 
 
=> (  ( sqaure root 2 ) - 1) 2 /  ( ( sqaureroot 2 )2 - 12 )
{ using (a+b)(a-b) = a2 - b2 }
 
=>  ( ( sqaure root 2 ) - 1 ) / (2-1)
=> ( sqaure root 2 ) - 1  Answer 
Answered by Expert 28th July 2012, 6:35 PM
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