if  root 3 tan theta = 3 sin theta, then ( sin2 thea - cos2 theta) = ??

since root 3 tan theta = 3sin theta

so, root 3 son theta /cos theta= sin theta

= so, root 3 will cut 3 and sin theta wil be cancelled

= so, 1/cos theta= root3

so, cos theta =1/root 3

so, squaring on both sides:

=cos2theta= 1/3

let it be equation no. 1

 

= 1-sin2theta= 1/3

=sin 2 theta=1-1/3

= sin2theta=2/3

let it be equation no. 2

so, on subtracting equation 1 from 2:

sin2theta - cos2theta = 22/32 - 12/32

                                       = 4/9 - 1/9

                                       = 3/9 = 1/3 that is the answer.

i hope you may be satisfied with my answer.

thumbs up if u like it plzzzzz

thank you.

  • 184

 it can also b written as 

root3   sin theta  / cos theta     =  3 sin  theta 

 cos  theta =  1/ root3 

sin  theta =  sq. root of  1- cos2 theta 

sin theta = root  (2/3)

 put values  and solve 

ans is 1/3

  • 29
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