Prove that `cot12^(@)cot38^(@)cot52^(@)cot78^(@)cot60^(@)=(1)/(sqrt3)`

cot10^(@)cot20^(@)cot60^(@)cot70^(@)cot80^(@)=

cot6^(0)cot42^(0)cot66^(@)cot78^(@)=1

cot780^(@)=cot(2xx360^(@)+60^(@)) =cot60^(@)=(1)/(sqrt(3))

cot12^(@)cot102^(@)+cot102^(@)cot66^(@)+cot66^(@)cot12^(@) =

Find the value of cot 12^@ cot38^@cot 52^@cot78^@cot60^@ .

Prove that cot^(-1)7+cot^(-1)8+cot^(-1)18=cot^(-1)3

Evaluate each of the following: cot12^(@)cot38^(@)cot52^(@)cot60^(@)cot78^(@)tan5^(@)tan25^(@)tan30^(@)tan65^(@)tan85^(@)

Prove that : (i) tan 5^@tan 25^@ tan 30^@tan 65^@tan 85^@=(1)/(sqrt(3)) (ii) cot 12^@cot38^@cot 52^@cot60^@cot78^@=(1)/(sqrt(3)) (iii) cos 15^@cos 35^@cosec 55^@cos 60^@cosec 75^@=(1)/(2) (iv) cos 1^@cos 2^@cos 3^@.....cos 180^@=0 (v) ((sin 49^@)/(cos 41^@))^2+ ((cos 41^@)/(sin 49^@))^2=2

Without using trigonometric tables, prove that : (i) tan 48^@tan 23^@tan 42^@tan 67^@ =1 (ii) tan 7^@tan 23^@ tan 60^@ 67^@tan 83^@=sqrt(3) (iii) cot 12^@cot 38^@cot 52^@cot 60^@cot 78^@=(1)/(sqrt(3))

Prove that : cot^(-1)7+cot^(-1)8+cot^(-1)18=cot^(-1)3