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

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

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

Prove that 4/3cot^2 30^@+3sin^2 60^@-2cosec^2 60^@-3/4tan^2 30^@=10/3

Prove that : (4)/(3) tan ^(2) 30^(@) + sin ^(2) 60^(@) - 3 cos ^(2) 60^(@) + (3)/(4) tan^(2) 60^(@) - 2 tan^(2) 45^(@) = (25)/(36)

Prove that : cosec 60^@ cot 30^@ tan 60^@= 2 sec^2 45^@ cos30^@ .

Prove that cot12^(@)cot38^(@)cot52^(@)cot78^(@)cot60^(@)=(1)/(sqrt3)

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