Question

prove that tan@tan(60-@)tan(60+@)=tan3@.
here"@" is taken as "theta".

Answer 1

\[\tan(60-t)\tan(60+t) = (\sqrt3 - tant)(\sqrt3 + tant)/(1 + \sqrt3 tant)(1- \sqrt3 tant)\]

Answer 2

\[= (3 - \tan^{2} t)/ (1 - 3\tan^{2}t)\]

Answer 3

now multiply that by tan t

u get

\[(3tant - \tan ^{3} t)/ (1 - 3\tan^{2} t) \ which \ is \ equal \ t o \ \tan 3t\]

Answer 4

thxx