Consider the equation
`log_(sqrt(2)sinx) (1 + cos x) = 2, x in [-(pi)/2, (3pi)/2]`.If the sum of the roots is `(p pi)/(q)`, where G.C.D (p,q) = 1 then the value of `p^(2) + q^(2)`is

If cos x*cos2x*cos4x*cos8x for x=(2 pi)/(3) is a rational number (p)/(q) where p,q in N .then the least value of (p+q) is

If sum of all the solutions of the equation (4tan x+tan^(2)x+1)=2sqrt(2)sin(x+(pi)/(4))(1+tan^(2)x) in [0,pi] is (p, (pi)/(q)) where p,q are relatively prime number, then find the value of (p+q)

If cos^(-1)p+cos^(-1)q+cos^(-1)r=pi(0<=p,q,r<=1) then the value of p^(2)+q^(2)+r^(2)+2pqr is

If 3 - 4i is a root of x^(2) - px + q = 0 where p, q in R . then value (2 p - q)/( p + q) is

If the roots of the equation 2x^(2)+7x+4=0 are in the ratio p:q, then the value of sqrt((p)/(q))+sqrt((q)/(p))

If equation 6(log_(x)2-log_(4)x)+7=0 has roots x_(1) and x_(2) then log_(2)x_(1)x_(2) is equal to (p)/(q) , where p and q are co-prime numbers, then the value of p+q is equal to

The expression log_(2)5-sum_(k=1)^(4)log_(2)(sin((k pi)/(5))) reduces to (p)/(q) where p and q are co-prime,the value of p^(2)+q^(2) is

With usual notations in Delta ABC ,let /_A=60^(0) and b , c are roots of the equation x^(2)-2sqrt(3)x+1=0. If the value of sum(a+b) cos C equals p+2sqrt(q) , where p,q in N, then find the value of (p+q)