If `tan(37.5)^@=sqrta-sqrtb+sqrtc-sqrtd,` where, `a,b,c,d in N and a > b > c > d` then the value of `(abc)/d` is

If the value of the definite integral int ^(-1) ^(1) cos ^(-1) ((1)/(sqrt(1-x ^(2)))) . (cot ^(-1)""(x )/(sqrt (1-(x ^(2))^(|x|))))dx = (pi^(2)(sqrta-sqrtb))/(sqrtc) where a,b,c in N in their lowest from, then find the value of (a+b+c).

If A=[[a,b] , [c,d]] and B=[[a',b] , [c',d']] then find the value of A-B

If int_(pi/4)^(pi/3) ((sin^3theta-cos^3theta-cos^2theta)(sintheta+costheta+cos^2theta)^2007)/((sintheta)^2009( costheta)^2009))d theta=((a+sqrtb)^n-(1+sqrtc)^n)/d where a,b,c,d are all positive integers. Find the value of (a+b+c+d).

Prove that sqrta-sqrtb irrational where a,b are primes.

If a sec a-c tan a=d and b sec a+d tan a=c then

Let sqrta+sqrtd=sqrtc+sqrtb and ad=bc , where a, b, c, in R^(+) . If the family of lines (a^(2)x+b^(2)y+c^(2))+d^(2)x=0 passes through a fixed point (x_(0), y_(0)) , then the value of (x_(0)+y_(0)) is

Let sqrta+sqrtd=sqrtc+sqrtb and ad=bc , where a, b, c, in R^(+) . If the family of lines (a^(2)x+b^(2)y+c^(2))+d^(2)x=0 passes through a fixed point (x_(0), y_(0)) , then the value of (x_(0)+y_(0)) is

If (c)/(d)-(a)/(b)=x, a=2c, and b=5d , what is the value of (c)/(d) in terms of x?