`tan 75 ^(@) - tan 30^(@)- tan 75^(@) tan 30^(@) =1.`

Show that : (i) tan 10^(@) tan 15^(@) tan 75^(@) tan 80^(@) = 1 (ii) sin 42^(@) sec 48^(@) + cos 42^(@) "cosec 48"^(@) = 2

Show that: tan 10^(@)tan 15^(@) tan 75^(@)tan 80^(@)=1

tan 6 ^(@) tan 42 ^(@) tan 66 ^(@) tan 78^(@) =1

Find (in each case, given below) the value of x, if : tan x = (tan 60^(@) - tan 30^(@))/(1 + tan 60^(@) tan 30^(@))

Solve (sin 10^(@))^(tan x+tan 3x)=tan 15^(@)+tan 30^(@)+ tan 15^(@). Tan 30^(@), x in (0, pi] .

Show that tan48^(@) tan 23^(@) tan 42^(@) tan 67^(@) =1 .

If tan 35^(@) = k , then the value of ( tan 145^(@) - tan 125^(@))/(1+ tan 145^(@) tan 125^(@)) =

Evaluate (tan60^(@)-tan30^(@))/(1+tan60^(@)tan30^(@)) .

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

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