Question

To proove

tan2a-tana=tanasec2a​

Answer 1

hey maye:

prove here

tan (2a) - tan a = tan (a ) sec (2a)

proof:-

Take L.H.S.

= tan 2a - tan a

= tan (a + a )- tan a

= (tan a + tan a)/(1- tan a × tan a) - tan a

= [2tan a/ (1- tan ^2 a]- tan a

= tan a [ 2/(1 - tan ^2 a) - 1]

=tan a[ 2 - 1 + tan^2 a]/(1 - tan ^2 a)

= tan a [ (1+ tan ^2 a )/1- sin ^2 a /cos^2 a)]

= tan a [ sec^2 a /(cos^2 a - sin^2 a)/cos^2 a

= tan a [ (sec^2 / cos 2 a)] × cos ^2 a

= tan a /cos2a

= tan a sec 2a.

= R.H.S.

uses sum formula

1) sec^2 a - tan^2 a = 1

2) cos^2 a - sin^2 a = cos 2a.

3) cos a = 1/sec a.

i hopes its helps u.

please follow me!!

@abhi.