If `p >1` and `q >1` are such that `log(p+q)=logp+logq ,`then the value of `log(p-1)+log(q-1)` is equal to

If sin A +cos A =p and tan A +cot A=q , then the value of q(p^2-1) will be

For 0 le P, Q le (pi)/(2) , if sin P+cos Q=2 , then the value of tan((P+Q)/(2)) is equal to

If P is the number of natural numbers whose logarithms to the base 10 have the the charecteristic p and Q is the numbers of natural numbers logarithms of whose reciprocal to the base 10 have the charecteristics -q. then find the value of log_(10) P-log_(10) Q

If log_(p)x=a and log_(q)x=b prove that log_(p/q)x=(ab)/(a-b)

If p,q,r three complex nos. so that p+q+r =0 and abs(p)=abs(q)=absr=1 then the value of (1/p+1/q+1/r) is

If p and q are positive, then prove that the coefficients of x^p and x^q in the expansion of (1+x)^(p+q) will be equal.

Let p , q , r be the altiudes of triangles with area s and perimeter 2 t . Then the value of (1)/(p)+(1)/(q)+(1)/(r) is _

If a, b, c are respectively the p-th, q-th, r-th terms of an A.P. then the value of |(a,p,1),(b,q,1),(c,r,1)| is -

Factorise : p^(2)+2p-(q+1)(q-1)

Factorise : p^(2)+2p-(q+1)(q-1)