" 40.Prove that "(sqrt(3)+1)(3-cot30^(@))=tan^(3)60^(@)-2sin60^(@).

Prove that sqrt((1+cos30^(@))/(1-cos30^(@)))=sec 60^(@)+tan60^(@) .

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

Prove that sqrt((1+cos30^@)/(1-cos30^@))=sec 60^@+tan 60^@ .

Prove that: cot A+cot(60^(@)+A)-cot(60^(@)-A)=3cot3A

Prove that: tan A+tan(60^(@)+A)-tan(60^(@)-A)=3tan3A

Prove (1-sin60^(@))/(cos60^(@))=(1-tan30^(@))/(1+tan30^(@))

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

Prove that: (cos30^(@)+sin60^(0))/(1+cos60^(@)+sin30^(@))=(sqrt(3))/(2)

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

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