`tan9^(@)-tan27^(@)-tan63^(@)+tan81^(@)=`

tan9^(0)-tan27^(0)-tan63^(@)+tan81^(@)

Prove that: (i) "sin"^(2)24^(@)-"sin"^(2)6^(@)=(1)/(8)(sqrt(5)-1) (ii) "tan"9^(@)-"tan"27^(@)-"tan"63^(@)+"tan"81^(@)=4 .

Statement-1: sin^(2)6^(@) + sin^(2)12^(@) + sin^(2)18^(@) +……..+ sin^(2)84^(@)=7 Statement-2: tan9^(@) tan27^(@) tan45^(@) tan36^(@) tan81^(@)=1 Statement-3: (tan(pi/4) + cot(pi/4) + " cosec " pi/4) (tan(pi/4) + cot(pi/4) - " cosec "pi/4) = sec ^(2)pi/3

tan 9^(@) - tan 27^(@) - tan 63^(@) + tan 81^(@)=.................. ??

Calculate the following without using trigonometric tables (i) tan 9^(@) - tan 27^(@) - tan 63^(@) + tan 81^(@) (ii) cosec 10^(@) -sqrt(3) sec 10^(@) (iii) 2sqrt(2) sin 10^(@) [(sec 5^(@))/(2) + (cos 40^(@))/(sin 5^(@))-2 sin 35^(@)] (iv) cot 70^(@)+4 cos 70^(@)

What is the value of (tan 9^(@) tan 23^(@) tan 60^(@) tan67^(@) tan 81^(@))/("cosec"^(2)72^(@)+cos^(2)15^(@)-tan^(2)18^(@)+cos^(2)75^(@))? (a) (1)/(2 sqrt(3)) (b) (sqrt(3))/(2) (c) (1)/(sqrt(3)) (d) 2 sqrt(3)