`tan20^@+tan40^@+sqrt3 tan20^@ tan40^@=` `(a).sqrt3/4 (b).sqrt3/2 (c).sqrt3 (d).1`

tan 70^(@) -tan 20^(@) - 2 tan 40^(@) = 4 tan 10 ^(@).

Prove that sin 20^(@) sin 40^(@) sin 80^(@) = (sqrt3)/(8).

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 tan 7 (1^(@))/(2) = sqrt2 - sqrt3 -sqrt4 + sqrt6 = (sqrt3 - sqrt2) (sqrt2 -1).

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

Prove that : tan 20^0 tan 40^0 tan 60^0 tan 80^0 =3

The value of (1-tan^2 15^@)/(1+tan^2 15^@)= (A) 1 (B) sqrt(3) (C) sqrt(3)/2 (D) 2

If tan^(-1)x+2cot^(-1)x=(2pi)/3, then x , is equal to (a) (sqrt(3)-1)/(sqrt(3)+1) (b) 3 (c) sqrt(3) (d) sqrt(2)

tan5oxxtan30oxx4tan85o is equal to 4/(sqrt(3)) (b) 4sqrt(3) (c) 1 (d) 4

Prove that, cot 7 1/2 ^@ or tan 82 1/2 ^@ = (sqrt(3)+sqrt(2))(sqrt(2)+1) or sqrt(2)+sqrt(3)+sqrt(4)+sqrt(6)