Question

Find the exact value of tan^2 30º - csc^2 30º.

Answer 1

=13/3

Answer 2

@Loser66 would you please explain for me how you got it. Thank you :)

Answer 3

sec^2x-tan^2x=1

Answer 4

sec^2x+1=tan^2x
sec^2x+1-csc^2x=1+sec^2x-cosec^2x

Answer 5

\[\sec30=\frac{ \sqrt{3} }{ 2 }\]

Answer 6

and find square of it
similarly csc 30=1/sin30
and find square of it and put in equation

Answer 7

@gorv thank you.

Answer 8

I don't know why we have to do something more, I just take tan (30) = \(\sqrt 3\) so that tan^2 (30) =3
and + with \(sec =\dfrac{1}{cos (30)}= \dfrac{1}{\sqrt3/2} =\dfrac{2}{\sqrt3}\) which gives me sec^2 = 4/3
hence tan^2 (30) + sec^2 (30)= 3+ 4/3 = 13/3