Prove that: `tan20^@tan35^@tan45^@tan55^@tan70^@=1`

Prove that: tan10^(@)tan50^(@)+tan50^(@)tan70^(@)+tan70^(@)tan170^(@)=3

Without using trigonometric tables , prove that : (i) tan20^(@)tan40^(@) tan45^(@)tan50^(@)tan70^(@)=1 (ii) tan1^(@) tan2^(@)tan60^(@)tan88^(@)tan89^(@)=sqrt(3) (iii) cot5^(@)cot10^(@)cot30^(@)cot80^(@)cot85^(@)=sqrt(3) (iv) 4sin10^(@)sin20^(@)sin30^(@)sec70^(@)sec80^(@)=2

Prove that tan70^0=2tan50^0+tan20^0

Prove that: tan20^0tan40^0tan80^0=tan60^0

Prove that: (a) tan 20^(@)tan40^(@)tan60^(@)tan 80^(@)=3 (b) tan9^(@)-tan27^(@)-tan63^(@)+tan81^(@)=4

Prove that tan20^0tan40^0tan80^0=tan60^0

Prove that: tan10^(@) tan20^(@)tan70^(@)tan80^(@)=1

Prove that: i) tan36^(@)+tan9^(@)+tan36^(@)tan9^(@)=1

Prove that tan 12^@ tan 24^@ tan 48^@ tan 84^@ = 1 .

Prove that: tan6^0tan42^0tan66^0tan78^0=1.