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The Value of Tan 60 Degree

The value of tan 60 and 30 degree

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The Value of Tan 60 Degree

Question:-`(tan 60^@-tan 30^@)/(1+tan 60^@tan 30^@) = tan 30`

LHS:
(tan 60 degree- tan 30 degree)/ ( 1+ tan 60 degree* tan 30 degree)
Now,
The value of tan 60 degree= root 3
The value of tan 30 degree= 1/ root 3
Hence, tan 60 degree- tan 30 degree = (root 3 – (1/ root 3))
= (3-1)/ root 3 [As root 3* root 3 = 3]
= 2/ root 3

Now, 
( 1+ tan 60 degree* tan 30 degree)
= (1+ ( root 3*1/ root 3))
=1+1 [root 3*1/ root 3= 1]
=2

Hence, LHS= (( 2/ root 3)/ 2)
= 1/ root 3
= tan 30 degree [ As The value of tan 30 degree= 1/ root 3]

Hence LHS= RHS (Proved)

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