prove that `6^(1//2)xx6^(1//4)xx6^(1//8)…oo=6`

If sqrt(1-x^6)+sqrt(1-y^6)=a(x^3-y^3), then prove that (dy)/(dx)=(x^2)/(y^2)sqrt((1-y^6)/(1-x^6))

Prove that cos 2 0^(@)cos4 0^(@)cos6 0^(@)cos8 0^(@)=1/16

Look at the following pattern : (i) 28 = 2^(2) xx 7^1 , Total number of factors (2+1) (1+1)= 3 xx 2 =6 28 is divisble by 6 factors i.e., 1,2,4,7,14,28 (ii) 30=2^(1) xx 3^(1) xx 5^(1) , Total number of factors ( 1+1)(1+1)(1+1)=2 xx 2 xx 2 =8 30 is divisble by 8 factor i.e., 1,2,3,5,6,10,15,30

Value of (1+1/3)(1+1/(3^2))(1+1/(3^4))(1+1/(3^8))........oo is equal to a. 3 b. 6/5 c. 3/2 d. none of these