`tan60^(@)cos60^(@)+cot60^(@)sin60^(@)=_____`.

Find the value of sin60^(@)cos30^(@)+cos60^(@)sin30^(@) .

Prove that : sin60^(@)cos30^(@)+cos60^(@).sin30^(@)=1

Calculate : (tan60^(@)-tan30^(@))/(1+tan60^(@) tan30^(@))+cos60^(@) cos30^(@)+sin60^(@) sin 30^(@) .

Choose the correct option and justify your choice :(i)(2tan30^(@))/(1+tan^(2)30^(@))(a)sin60^(@)(b)cos60^(@)(c)tan60^(@)(d)sin30^(@)

Evaluate : (i) sin60^(@)*cos30^(@)-cos60^(@)*sin30^(@) (ii) tan30^(@)*cosec60^(@)+tan60^(@)*sec30^(@) .

(tan60^@)/(sin60^@+cos30^@)

If x tan 30^(@) = (sin 30^(@) + cos 60^(@))/( tan 60^(@) + sin 60^(@)) , then the value of x is :

Prove that : cos30^(@).cos60^(@)-sin30^(@).sin60^(@)=0

Prove that : cos30^(@).cos60^(@)-sin30^(@).sin60^(@)=0

Show that : (i) (1-sin60^(@))/(cos60^(@))=(tan60^(@)-1)/(tan60^(@)+1) (ii) (cos30^(@)+sin60^(@))/(1+sin30^(@)+cos60^(@))=cos30^(@)