`(2tan30^(@))/(1+tan^(2)30^(@))=?`

Verify that sin60^(@)=(2tan 30^(@))/(1+tan^(2)30^(@))

Verify that cos 60^(@)=(1-tan^(2)30^(@))/(1+tan^(2)30^(@))

Prove that : cos(2 times 30^(@))=(1-tan^(2)30^(@))/(1+tan^(2)30^(@))

Prove that : cos(2 times 30^(@))=(1-tan^(2)30^(@))/(1+tan^(2)30^(@))

(2tan3 0^(@))/(1-tan^2 3 0^(@)) is equal to (a) sin60^(@) (b) cos60^(@) (c) tan60^(@) (d) sin30^(@)

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

Prove that (4)/(3)cot^(2)30^(@)+3sin^(2)60^(@)-2" cosec"^(2)60^(@)-(3)/(4)tan^(2)30^(@)=3(1)/(3) .

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

Prove that : ((tan60^(@)+1)/(tan60^(@)-1))^(2)=(1+cos30^(@))/(1-cos30^(@))

Show that : 2tan^(2)60^(@)-6(sin^(2)45^(@)-tan^(2)30^(@))=5